Real_World_Weighted_Crossentropy_Loss_Function.ipynb

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  "metadata": {
    "colab": {
      "name": "Real-World-Weighted Crossentropy Loss Function",
      "provenance": [],
      "collapsed_sections": [
        "_27cHEGCUMiB"
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      "machine_shape": "hm",
      "include_colab_link": true
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    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/yaoshiang/The-Real-World-Weight-Crossentropy-Loss-Function/blob/master/Real_World_Weighted_Crossentropy_Loss_Function.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5Y1dlLOBjGuy",
        "colab_type": "text"
      },
      "source": [
        "# Real-World-Weighted Crossentropy Loss Function\n",
        "\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pjW5dVQjjE6d",
        "colab_type": "text"
      },
      "source": [
        "This is a companion notebook to the paper published at <<<>>>."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mOo8TfTRUIOX",
        "colab_type": "text"
      },
      "source": [
        "Copyright (C) 2019 Yaoshiang Ho\n",
        "\n",
        "This program is free software: you can redistribute it and/or modify\n",
        "it under the terms of the GNU General Public License as published by\n",
        "the Free Software Foundation, either version 3 of the License, or\n",
        "(at your option) any later version.\n",
        "\n",
        "This program is distributed in the hope that it will be useful,\n",
        "but WITHOUT ANY WARRANTY; without even the implied warranty of\n",
        "MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n",
        "GNU General Public License for more details.\n",
        "\n",
        "Contact author for exceptions. \n",
        "\n",
        "You should have received a copy of the GNU General Public License\n",
        "along with this program.  If not, see <https://www.gnu.org/licenses/>."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2G2rcSxFUBVY",
        "colab_type": "text"
      },
      "source": [
        "## Setup"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "r6B-pD4hiHyi",
        "colab_type": "code",
        "outputId": "53082ef5-6cc9-4396-c6d4-2001de2ff7f4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        }
      },
      "source": [
        "# Import necessary libraries\n",
        "\n",
        "from sklearn.datasets import fetch_openml\n",
        "from sklearn.model_selection import train_test_split\n",
        "\n",
        "import numpy as np\n",
        "from numpy.random import seed\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "%tensorflow_version 1.x\n",
        "import tensorflow as tf\n",
        "print(tf.__version__)\n",
        "\n",
        "from tensorflow import set_random_seed\n",
        "\n",
        "import keras.backend as K\n",
        "from keras.layers import Input, Dense, Dropout\n",
        "from keras.models import Model\n",
        "from keras.utils import to_categorical\n",
        "from keras.optimizers import SGD\n",
        "\n",
        "import scipy as sp\n",
        "\n",
        "from tabulate import tabulate\n",
        "\n",
        "import datetime\n",
        "\n",
        "np.set_printoptions(formatter={'float': lambda x: \"{0:0.2f}\".format(x)})"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "1.15.0\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "Using TensorFlow backend.\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5uUw19MXj_tb",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Fetch MNIST dataset\n",
        "\n",
        "mnist = fetch_openml('mnist_784', cache=True)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Q6GkBRRwkHbl",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#Processing on MNIST data\n",
        "X = mnist.data.astype('float32')\n",
        "y = mnist.target.astype('int64')\n",
        "X /= 255.0\n",
        "X = X\n",
        "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.25, random_state=1)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_27cHEGCUMiB",
        "colab_type": "text"
      },
      "source": [
        "## The Real-World-Weight Crossentropy loss functions for binary and categorical\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KTJE_umwrIRp",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Copyright (C) 2019 Yaoshiang Ho\n",
        "\n",
        "# This program is free software: you can redistribute it and/or modify\n",
        "# it under the terms of the GNU General Public License as published by\n",
        "# the Free Software Foundation, either version 3 of the License, or\n",
        "# (at your option) any later version.\n",
        "#\n",
        "# This program is distributed in the hope that it will be useful,\n",
        "# but WITHOUT ANY WARRANTY; without even the implied warranty of\n",
        "# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n",
        "# GNU General Public License for more details.\n",
        "#\n",
        "# Contact author for exceptions.\n",
        "#\n",
        "# You should have received a copy of the GNU General Public License\n",
        "# along with this program.  If not, see <https://www.gnu.org/licenses/>.\n",
        "\n",
        "def create_rww_binary_crossentropy(fn_weight, fp_weight):\n",
        "  \"\"\"\n",
        "  binary_crossentropy is a special case of categorical_crossentropy.  \n",
        "  The \"all other\" column is imputed. For single-label, an implementation is provided.\n",
        "  However, this loss function is not very useful in a multi-label environment. \n",
        "  It only supports k=1. \n",
        "  \n",
        "  In future work, we will provide an implementation for one target, \n",
        "  one miscategorization. Note that this will\n",
        "  require a tensor of at lease size (k,k,2,2), where, the first 2 \n",
        "  represents T/F of target, the second 2 represents the FP/FN of label. \n",
        "\n",
        "  We may also create a fully expressive loss function, which would require some\n",
        "  efficient representation of a tensor of size (k, k, 2^k, 2^k)\n",
        "  \n",
        "  \"\"\"  \n",
        "  def binary_loss_function(target, output):\n",
        "    output = K.clip(output, K.epsilon(), 1 - K.epsilon()) \n",
        "    \n",
        "    logs = K.log(output) # shape (m, 1)\n",
        "    logs_1_sub = K.log(1-output) # shape (m, 1)\n",
        "\n",
        "    return - K.mean(target * fn_weight * logs + \n",
        "                    (1-target) * fp_weight * logs_1_sub)\n",
        "\n",
        "  return binary_loss_function\n",
        "\n",
        "def create_rww_categorical_crossentropy(k, loss_type, fn_weights=None, fp_weights=None, return_weights=False):\n",
        "  \"\"\"Real-World-Weighted crossentropy between an output tensor and a target tensor.\n",
        "  \n",
        "  The loss_types other than rww_categorical_crossentropy reimplement existing \n",
        "  functions in Keras but are not as well optimized. \n",
        "  These loss_types are usable directly, but, are more useful when calling \n",
        "  return_weights=True, which then returns fn and fp weights matrixes of size (k,k). \n",
        "  Editing those to reflect real world costs, then passing them back into \n",
        "  create_rww_crossentropy with loss_type \"rww_crossentropy\" is the recommended approach. \n",
        "\n",
        "  Example Usage: \n",
        "\n",
        "  Suppose you have three classes: cat, dog, and other.\n",
        "  \n",
        "  Cat is one-hot encoded as [1,0,0], dog as [0,1,0], other as [0,0,1]\n",
        "  \n",
        "  The the following code increases the incremental penalty of \n",
        "  mislabeling a true target 0 (cat) with a false label 1 (dog) at a cost of 99, \n",
        "  versus the default of zero. Note that the existing fn_weights also has a \n",
        "  default cost of 1 for missing the true target of 1, for a total cost of \n",
        "  100 versus the default cost of 1. \n",
        "  \n",
        "  fn_weights, fp_weights = create_rww_categorical_crossentropy(10, \"categorical_crossentropy\", return_weights=True)\n",
        "  fp_weights[0, 1] = 99\n",
        "  loss = create_rww_categorical_crossentropy(10, \"rww_crossentropy\", fn_weights, fp_weights)\n",
        "\n",
        "... \n",
        "  \n",
        "  The fn and fp weights are easy to reason about. \n",
        "  \n",
        "  fn_weights is [x1, __, __]\n",
        "                [__, x2, __]\n",
        "                [__, __, x3]\n",
        " \n",
        "  x1 represents the scale of the cost for a fn for cat, x2 for dog, and x3 for other.\n",
        "  \n",
        "  This is calculated as fn_weight * log(y_pred). \n",
        "  \n",
        "  In the case of loss_type=categorical_crossentropy, \n",
        "  x1, x2, and x3 all equal the value one. \n",
        "  All elements not on the main axis must equal zero. \n",
        "  \n",
        "  Note that fn_weights could have been represented as a vector, \n",
        "  not a matrix, however, we use a matrix to keep symmetry with \n",
        "  fp_weights, and, to prepare for \n",
        "  multi-label classification. \n",
        "    \n",
        "  ...\n",
        "\n",
        "  fp_weights is concerned with the costs of the fps from the other classes. \n",
        "\n",
        "  fp_weights of [__, x1, x2]\n",
        "                [x3, __, x4]\n",
        "                [x5, x6, __]\n",
        " \n",
        "  x1 represents the cost of predicting 1 for dog, when it should be 0 for cat. \n",
        "  x2 represents predicting 2 for other, when the target is 0 for cat. \n",
        "  x3 represents predicing 0 for cat, when the target is 1 for dog.\n",
        "  etc. \n",
        "  \n",
        "  Args:\n",
        "    * k: 2 or more for number of categories, including \"other\". \n",
        "    * loss_type: \"categorical_crossentropy\" to initialize to \n",
        "      standard softmax_crossentropy behavior, \n",
        "      or \"weighted_categorical_crossentropy\" for standard behavior, or, \n",
        "      or \"rww_crossentropy\" for full weight matrix of all possible fn/fp combinations. \n",
        "    * fn_weights: a numpy array of shape (k,k). The main diagonal can\n",
        "      contain non-zero values; all other values must be zero. \n",
        "    * fp_weights: a numpy array of shape (k,k) to define specific combinations \n",
        "      of false positive. The main diag should be zeros. \n",
        "    * return_weights: If False (default), returns cost function. If True, \n",
        "      returns fn and fp weights as np.array. \n",
        "Returns:\n",
        "    * retval: Loss function for use Keras.model.fit, or if return_weights\n",
        "      arg is True, the fn_weights and fp_weights matrixes. \n",
        "  \"\"\"\n",
        "\n",
        "  full_fn_weights = None\n",
        "  full_fp_weights = None\n",
        "\n",
        "  anti_eye = np.ones((k,k)) - np.eye(k)\n",
        "    \n",
        "  if (loss_type==\"categorical_crossentropy\"):\n",
        "    full_fn_weights = np.identity((k))\n",
        "    full_fp_weights = np.zeros((k, k)) # Softmax crossentropy ignores fp.\n",
        "\n",
        "  elif(loss_type==\"weighted_categorical_crossentropy\"):\n",
        "    full_fn_weights = np.eye(k) * fn_weights\n",
        "    full_fp_weights = np.zeros((k, k)) # softmax crossentropy ignores fp\n",
        "    \n",
        "  elif(loss_type==\"rww_crossentropy\"):\n",
        "    assert not np.count_nonzero(fn_weights * anti_eye)\n",
        "    assert not np.count_nonzero(fp_weights * np.eye(k))\n",
        "\n",
        "    full_fn_weights = fn_weights\n",
        "    # Novel piece: allow any combination of fp.\n",
        "    full_fp_weights = fp_weights\n",
        "    \n",
        "  else:\n",
        "    raise Exception(\"unknown loss_type: \" + str(loss_type))\n",
        "   \n",
        "  fn_wt = K.constant(full_fn_weights) # (k,k), always sparse along main diag. \n",
        "  fp_wt = K.constant(full_fp_weights) # (k,k), always dense except main diag. \n",
        "\n",
        "  def loss_function(target, output):\n",
        "    output = K.clip(output, K.epsilon(), 1 - K.epsilon()) \n",
        "    \n",
        "    logs = K.log(output) # shape (m, k), dense. 1 is good. \n",
        "    logs_1_sub = K.log(1-output) # shape (m, k), dense. 0 is good. \n",
        "\n",
        "    m_full_fn_weights = K.dot(target, fn_wt) # (m,k) . (k, k)\n",
        "    m_full_fp_weights = K.dot(target, fp_wt) # (m,k) . (k, k)\n",
        "\n",
        "    return - K.mean(m_full_fn_weights * logs + \n",
        "                    m_full_fp_weights * logs_1_sub)\n",
        "  \n",
        "  if (return_weights):\n",
        "    return full_fn_weights, full_fp_weights\n",
        "  else:\n",
        "    return loss_function"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "s8uIO9axuDkW",
        "colab_type": "code",
        "outputId": "190df142-facc-4205-aecd-b5d3341a1a01",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 765
        }
      },
      "source": [
        "# Example of categorical_crossentropy. Class behavior. \n",
        "fn_weights, fp_weights = create_rww_categorical_crossentropy(5, 'categorical_crossentropy', return_weights=True)\n",
        "print(\"softmax cross entropy weights. k=5 classes. Expected output: fn: ones, fp:zeros. \")\n",
        "print (fn_weights)\n",
        "print (fp_weights)\n",
        "\n",
        "# Example of weighted single-label categorical crossentropy. \n",
        "fn_weights, fp_weights = create_rww_categorical_crossentropy(5, 'weighted_categorical_crossentropy', np.array([1,2,3,4,5]), return_weights=True)\n",
        "print(\"weighted softmax crossentropy. k=5 classes. Expected output: fn: weights, fp: zeros. \")\n",
        "print (fn_weights)\n",
        "print (fp_weights)\n",
        "\n",
        "\n",
        "# Example of full weighted multi-label categorical crossentropy\n",
        "fn_weights, fp_weights = create_rww_categorical_crossentropy(10, \"categorical_crossentropy\", return_weights=True)\n",
        "fp_weights[5, 8] = 19\n",
        "loss = create_rww_categorical_crossentropy(10, \"rww_crossentropy\", fn_weights, fp_weights)\n",
        "print(\"real world weighted cross entropy weights. k=10 classes. If target label if 5, heavily penalize a (false positive) 8. \")\n",
        "print (fn_weights)\n",
        "print (fp_weights)\n",
        "\n",
        "print(loss)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "softmax cross entropy weights. k=5 classes. Expected output: fn: ones, fp:zeros. \n",
            "[[1.00 0.00 0.00 0.00 0.00]\n",
            " [0.00 1.00 0.00 0.00 0.00]\n",
            " [0.00 0.00 1.00 0.00 0.00]\n",
            " [0.00 0.00 0.00 1.00 0.00]\n",
            " [0.00 0.00 0.00 0.00 1.00]]\n",
            "[[0.00 0.00 0.00 0.00 0.00]\n",
            " [0.00 0.00 0.00 0.00 0.00]\n",
            " [0.00 0.00 0.00 0.00 0.00]\n",
            " [0.00 0.00 0.00 0.00 0.00]\n",
            " [0.00 0.00 0.00 0.00 0.00]]\n",
            "weighted softmax crossentropy. k=5 classes. Expected output: fn: weights, fp: zeros. \n",
            "[[1.00 0.00 0.00 0.00 0.00]\n",
            " [0.00 2.00 0.00 0.00 0.00]\n",
            " [0.00 0.00 3.00 0.00 0.00]\n",
            " [0.00 0.00 0.00 4.00 0.00]\n",
            " [0.00 0.00 0.00 0.00 5.00]]\n",
            "[[0.00 0.00 0.00 0.00 0.00]\n",
            " [0.00 0.00 0.00 0.00 0.00]\n",
            " [0.00 0.00 0.00 0.00 0.00]\n",
            " [0.00 0.00 0.00 0.00 0.00]\n",
            " [0.00 0.00 0.00 0.00 0.00]]\n",
            "real world weighted cross entropy weights. k=10 classes. If target label if 5, heavily penalize a (false positive) 8. \n",
            "[[1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00]\n",
            " [0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00]\n",
            " [0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00]\n",
            " [0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00]\n",
            " [0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00]\n",
            " [0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00]\n",
            " [0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00]\n",
            " [0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00]\n",
            " [0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00]\n",
            " [0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00]]\n",
            "[[0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00]\n",
            " [0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00]\n",
            " [0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00]\n",
            " [0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00]\n",
            " [0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00]\n",
            " [0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 19.00 0.00]\n",
            " [0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00]\n",
            " [0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00]\n",
            " [0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00]\n",
            " [0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00]]\n",
            "<function create_rww_categorical_crossentropy.<locals>.loss_function at 0x7f74a7ac0268>\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uKD5O2moUZWi",
        "colab_type": "text"
      },
      "source": [
        "## Testing Against Imbalanced Single-Label Multiclass (softmax)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eRdr4rjpk0G2",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def create_categorical_model(loss):\n",
        "  k_y = k_x = Input(shape=(784,))\n",
        "  k_y = Dense(50, activation='relu')(k_y)\n",
        "  k_y = Dense(20, activation='relu')(k_y)\n",
        "  k_y = Dense(10, activation='softmax')(k_y)\n",
        "\n",
        "  model = Model(inputs=k_x, outputs=k_y)\n",
        "  model.compile(optimizer='adam', loss=loss, metrics=['categorical_accuracy'])\n",
        "  return model\n",
        "\n",
        "# model_a = create_model(\"categorical_crossentropy\")\n",
        "# set_random_seed(1)\n",
        "# model_a.fit(x = X_train, y = to_categorical(y_train), epochs=10, batch_size=100, validation_split=0.1)\n",
        "# print(model_a.evaluate(X_test, to_categorical(y_test)))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XI-1L6elsVe2",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def average_predictions(z, y):\n",
        "  # Inputs: \n",
        "  #   z: raw output of softmax for m classes\n",
        "  #   y: target predictions\n",
        "  # Outputs:\n",
        "  #   average predictions matrix of size (z.shape[1],z.shape[1])\n",
        "  #     axis 0 are the true categories\n",
        "  #     axis 1 are the predicted categories\n",
        "  #     each cell is the average of the predictions\n",
        "  m, n = z.shape\n",
        "  y_pred = np.argmax(z, axis=1)  \n",
        "  \n",
        "  averages = np.zeros((n, n))\n",
        "  \n",
        "  for i in range(0, n):\n",
        "    mask = y == np.array(i)\n",
        "    assert mask.shape == (m,)\n",
        "    np.mean(z[mask], axis=0, out=averages[i])\n",
        "    \n",
        "  return averages\n",
        "\n",
        "# print(\"Average predictions for model_a. Rows are y, columns are y_hat\")\n",
        "# print(average_predictions(model_a.predict(X_test), y_test))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0QovfFnw4oVz",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def num_predictions(z, y):\n",
        "  # Inputs: \n",
        "  #   z: raw output of softmax for m classes\n",
        "  #   y: target predictions using argmax\n",
        "  # Outputs:\n",
        "  #   total predictions matrix of size (z.shape[1],z.shape[1])\n",
        "  #     axis 0 are the true categories\n",
        "  #     axis 1 are the predicted categories\n",
        "  #     each cell is the sum of the predictions\n",
        "  m, n = z.shape\n",
        "  y_pred = np.argmax(z, axis=1)  \n",
        "  \n",
        "  sums = np.zeros((n, n))\n",
        "  \n",
        "  for i in range(0, n):\n",
        "    mask = y == np.array(i)\n",
        "    assert mask.shape == (m,)    \n",
        "    np.sum(to_categorical(np.argmax(z[mask], axis=1), num_classes=10), axis=0, out=sums[i])\n",
        "  return sums\n",
        "\n",
        "# print(\"Total number of predictions for model_a. Rows are y, columns are y_hat\")\n",
        "# np.set_printoptions(formatter={'float': lambda x: \"{0:6.0f}\".format(x)})\n",
        "# print(num_predictions(model_a.predict(X_test), y_test))\n",
        "# np.set_printoptions(formatter={'float': lambda x: \"{0:0.2f}\".format(x)})"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "u58yBlElVaP9",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Calculate Real World Cost\n",
        "def clip_correct(preds):\n",
        "  k = preds.shape[0]\n",
        "  assert k == preds.shape[1]\n",
        "  \n",
        "  anti_eye = 1 - np.eye(k)\n",
        "  return preds * anti_eye # k,k, with the main diagonal masked out to zeros\n",
        "\n",
        "def categorical_real_world_cost(preds, fn_ws, fp_ws):\n",
        "  k = preds.shape[0]\n",
        "  assert k == preds.shape[1]\n",
        "  \n",
        "  false_preds = clip_correct(preds)\n",
        "  fn_cost = np.sum(np.sum(false_preds, axis=-1) * np.sum(fn_ws, axis=-1)) \n",
        "  fp_cost = np.sum(false_preds * fp_ws)\n",
        " \n",
        "  return (fn_cost + fp_cost) / np.sum(preds)\n",
        "\n",
        "def vector_categorical_real_world_cost(m, preds, fn_ws, fp_ws):\n",
        "  retval = np.zeros(m)\n",
        "  for i in range(0,m):\n",
        "    retval[i] = categorical_real_world_cost(preds[i], fn_ws[i], fp_ws[i])\n",
        "  return retval"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MuwzaTB3n75K",
        "colab_type": "code",
        "outputId": "3cb0c192-9383-47c4-b0ca-45370012ca15",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 870
        }
      },
      "source": [
        "def generate_unequal_pair(i):\n",
        "  np.random.seed(i)\n",
        "  a = np.random.randint(0, 10)\n",
        "  b = np.random.randint(0,10)\n",
        "  while a == b:\n",
        "    b = np.random.randint(0,10)\n",
        "  return a, b\n",
        "\n",
        "EPOCHS = 10 # We experimentally found no significant benefit after 10 epochs\n",
        "\n",
        "# For testing purposes only. Comment the following line out in typical usage. \n",
        "# EPOCHS = 1\n",
        "\n",
        "# Repeatability\n",
        "np.random.seed(1)\n",
        "set_random_seed(1)\n",
        "\n",
        "# Quick compare 10 sample and 10 control networks\n",
        "for i in range(0,10):\n",
        "  print(datetime.datetime.now(), end = \" \")\n",
        "  # Generate random socially biased or expensive fn,fp pair, setup rww_crossentropy loss function. \n",
        "  on_label, offensive_fp = generate_unequal_pair(i)  \n",
        "  fn_weights, fp_weights = create_rww_categorical_crossentropy(10, \"categorical_crossentropy\", return_weights=True)\n",
        "  fp_weights[on_label, offensive_fp] = 19\n",
        "  loss = create_rww_categorical_crossentropy(10, \"rww_crossentropy\", fn_weights, fp_weights)\n",
        "\n",
        "  # Train control model\n",
        "  model_control = create_categorical_model('binary_crossentropy') # K/TF builtin\n",
        "  model_control.fit(x = X_train, y = to_categorical(y_train), epochs=EPOCHS, batch_size=100, validation_split=0.1, verbose=0)\n",
        "  num_pred_control = num_predictions(model_control.predict(X_test), y_test)\n",
        "  _, acc_control = model_control.evaluate(X_test, to_categorical(y_test))\n",
        "  \n",
        "  # Train experimental model with same epochs / batchsize as control model. \n",
        "  model_test = create_categorical_model(loss) # RWW version\n",
        "  model_test.fit(x = X_train, y = to_categorical(y_train), epochs=EPOCHS, batch_size=100, validation_split=0.1, verbose=0)  \n",
        "  num_pred_test = num_predictions(model_test.predict(X_test), y_test)\n",
        "  _, acc_test = model_test.evaluate(X_test, to_categorical(y_test), verbose=0)\n",
        "\n",
        "  print(\"For test (fn:fp):(\" + str(on_label) + \",\" + \\\n",
        "        str(offensive_fp) + \"): FPs from (control, experimental): (\" + \\\n",
        "        str(num_pred_control[on_label, offensive_fp]) + \",\" +\\\n",
        "        str(num_pred_test[on_label, offensive_fp]) + \\\n",
        "        \"); Accuracy from (control, experimental):\" + \\\n",
        "        '{:0.4f}'.format(acc_control) + \",\", '{:0.4f}'.format(acc_test) + \")\")"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "2019-10-31 16:27:03.787544 WARNING:tensorflow:From /usr/local/lib/python3.6/dist-packages/keras/backend/tensorflow_backend.py:66: The name tf.get_default_graph is deprecated. Please use tf.compat.v1.get_default_graph instead.\n",
            "\n",
            "WARNING:tensorflow:From /usr/local/lib/python3.6/dist-packages/keras/backend/tensorflow_backend.py:541: The name tf.placeholder is deprecated. Please use tf.compat.v1.placeholder instead.\n",
            "\n",
            "WARNING:tensorflow:From /usr/local/lib/python3.6/dist-packages/keras/backend/tensorflow_backend.py:4432: The name tf.random_uniform is deprecated. Please use tf.random.uniform instead.\n",
            "\n",
            "WARNING:tensorflow:From /usr/local/lib/python3.6/dist-packages/keras/optimizers.py:793: The name tf.train.Optimizer is deprecated. Please use tf.compat.v1.train.Optimizer instead.\n",
            "\n",
            "WARNING:tensorflow:From /usr/local/lib/python3.6/dist-packages/keras/backend/tensorflow_backend.py:3657: The name tf.log is deprecated. Please use tf.math.log instead.\n",
            "\n",
            "WARNING:tensorflow:From /usr/local/lib/python3.6/dist-packages/tensorflow_core/python/ops/nn_impl.py:183: where (from tensorflow.python.ops.array_ops) is deprecated and will be removed in a future version.\n",
            "Instructions for updating:\n",
            "Use tf.where in 2.0, which has the same broadcast rule as np.where\n",
            "WARNING:tensorflow:From /usr/local/lib/python3.6/dist-packages/keras/backend/tensorflow_backend.py:1033: The name tf.assign_add is deprecated. Please use tf.compat.v1.assign_add instead.\n",
            "\n",
            "WARNING:tensorflow:From /usr/local/lib/python3.6/dist-packages/keras/backend/tensorflow_backend.py:1020: The name tf.assign is deprecated. Please use tf.compat.v1.assign instead.\n",
            "\n",
            "WARNING:tensorflow:From /usr/local/lib/python3.6/dist-packages/keras/backend/tensorflow_backend.py:3005: The name tf.Session is deprecated. Please use tf.compat.v1.Session instead.\n",
            "\n",
            "WARNING:tensorflow:From /usr/local/lib/python3.6/dist-packages/keras/backend/tensorflow_backend.py:190: The name tf.get_default_session is deprecated. Please use tf.compat.v1.get_default_session instead.\n",
            "\n",
            "WARNING:tensorflow:From /usr/local/lib/python3.6/dist-packages/keras/backend/tensorflow_backend.py:197: The name tf.ConfigProto is deprecated. Please use tf.compat.v1.ConfigProto instead.\n",
            "\n",
            "WARNING:tensorflow:From /usr/local/lib/python3.6/dist-packages/keras/backend/tensorflow_backend.py:207: The name tf.global_variables is deprecated. Please use tf.compat.v1.global_variables instead.\n",
            "\n",
            "WARNING:tensorflow:From /usr/local/lib/python3.6/dist-packages/keras/backend/tensorflow_backend.py:216: The name tf.is_variable_initialized is deprecated. Please use tf.compat.v1.is_variable_initialized instead.\n",
            "\n",
            "WARNING:tensorflow:From /usr/local/lib/python3.6/dist-packages/keras/backend/tensorflow_backend.py:223: The name tf.variables_initializer is deprecated. Please use tf.compat.v1.variables_initializer instead.\n",
            "\n",
            "17500/17500 [==============================] - 1s 40us/step\n",
            "For test (fn:fp):(5,0): FPs from (control, experimental): (0.0,0.0); Accuracy from (control, experimental):0.9640, 0.9621)\n",
            "17500/17500 [==============================] - 1s 42us/step\n",
            "For test (fn:fp):(5,8): FPs from (control, experimental): (9.0,3.0); Accuracy from (control, experimental):0.9643, 0.9531)\n",
            "17500/17500 [==============================] - 1s 42us/step\n",
            "For test (fn:fp):(8,6): FPs from (control, experimental): (7.0,3.0); Accuracy from (control, experimental):0.9659, 0.9619)\n",
            "17500/17500 [==============================] - 1s 46us/step\n",
            "For test (fn:fp):(8,9): FPs from (control, experimental): (7.0,6.0); Accuracy from (control, experimental):0.9653, 0.9643)\n",
            "17500/17500 [==============================] - 1s 45us/step\n",
            "For test (fn:fp):(7,5): FPs from (control, experimental): (2.0,0.0); Accuracy from (control, experimental):0.9634, 0.9627)\n",
            "17500/17500 [==============================] - 1s 44us/step\n",
            "For test (fn:fp):(3,6): FPs from (control, experimental): (2.0,0.0); Accuracy from (control, experimental):0.9615, 0.9629)\n",
            "17500/17500 [==============================] - 1s 47us/step\n",
            "For test (fn:fp):(9,3): FPs from (control, experimental): (6.0,5.0); Accuracy from (control, experimental):0.9637, 0.9629)\n",
            "17500/17500 [==============================] - 1s 48us/step\n",
            "For test (fn:fp):(4,9): FPs from (control, experimental): (30.0,16.0); Accuracy from (control, experimental):0.9623, 0.9652)\n",
            "17500/17500 [==============================] - 1s 49us/step\n",
            "For test (fn:fp):(3,4): FPs from (control, experimental): (1.0,1.0); Accuracy from (control, experimental):0.9637, 0.9620)\n",
            "17500/17500 [==============================] - 1s 50us/step\n",
            "For test (fn:fp):(5,6): FPs from (control, experimental): (14.0,5.0); Accuracy from (control, experimental):0.9610, 0.9655)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BguZppn4sMfJ",
        "colab_type": "code",
        "outputId": "11ad6c7f-49e6-40b1-84e8-27d838d84b7f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1547
        }
      },
      "source": [
        "# Train 90 control and 90 experimental models. \n",
        "\n",
        "# Repeatability\n",
        "np.random.seed(1)\n",
        "set_random_seed(1)\n",
        "\n",
        "accs = []\n",
        "fps = []\n",
        "preds = []\n",
        "ws = []\n",
        "\n",
        "for i in range(0,10):\n",
        "  for j in range (0,10):\n",
        "    if i == j: \n",
        "      continue\n",
        "\n",
        "    print(str(i*10 + j) + \":\" + str(datetime.datetime.now()))\n",
        "\n",
        "    fn_weights, fp_weights = create_rww_categorical_crossentropy(10, \"categorical_crossentropy\", return_weights=True)\n",
        "    fp_weights[i, j] = 19\n",
        "    loss = create_rww_categorical_crossentropy(10, \"rww_crossentropy\", fn_weights, fp_weights)\n",
        "\n",
        "    # Train control model\n",
        "    model_control = create_categorical_model('binary_crossentropy') # K/TF builtin\n",
        "    model_control.fit(x = X_train, y = to_categorical(y_train), epochs=EPOCHS, batch_size=100, validation_split=0.1, verbose=0)\n",
        "    num_pred_control = num_predictions(model_control.predict(X_test, verbose=0), y_test)\n",
        "    _, acc_control = model_control.evaluate(X_test, to_categorical(y_test), verbose=0)\n",
        " \n",
        "    # Train experimental model with same epochs / batchsize as control model. \n",
        "    model_test = create_categorical_model(loss) # RWW version\n",
        "    model_test.fit(x = X_train, y = to_categorical(y_train), epochs=EPOCHS, batch_size=100, validation_split=0.1, verbose=0)  \n",
        "    num_pred_test = num_predictions(model_test.predict(X_test, verbose=0), y_test)\n",
        "    _, acc_test = model_test.evaluate(X_test, to_categorical(y_test), verbose=0)\n",
        "\n",
        "    accs.append((acc_control, acc_test))\n",
        "    fps.append((num_pred_control[i, j], num_pred_test[i,j]))\n",
        "    preds.append((num_pred_control, num_pred_test))\n",
        "    ws.append((fn_weights, fp_weights))"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "1:2019-10-31 16:34:28.411562\n",
            "2:2019-10-31 16:35:15.641499\n",
            "3:2019-10-31 16:36:04.309588\n",
            "4:2019-10-31 16:36:53.598391\n",
            "5:2019-10-31 16:37:44.013906\n",
            "6:2019-10-31 16:38:35.755103\n",
            "7:2019-10-31 16:39:27.471340\n",
            "8:2019-10-31 16:40:19.238765\n",
            "9:2019-10-31 16:41:11.398103\n",
            "10:2019-10-31 16:42:04.525346\n",
            "12:2019-10-31 16:42:58.343883\n",
            "13:2019-10-31 16:43:53.783053\n",
            "14:2019-10-31 16:44:48.990590\n",
            "15:2019-10-31 16:45:45.556917\n",
            "16:2019-10-31 16:46:43.239585\n",
            "17:2019-10-31 16:47:41.491949\n",
            "18:2019-10-31 16:48:40.153569\n",
            "19:2019-10-31 16:49:39.483769\n",
            "20:2019-10-31 16:50:39.901936\n",
            "21:2019-10-31 16:51:40.507242\n",
            "23:2019-10-31 16:52:41.733563\n",
            "24:2019-10-31 16:53:44.510562\n",
            "25:2019-10-31 16:54:48.745278\n",
            "26:2019-10-31 16:55:53.604814\n",
            "27:2019-10-31 16:56:58.964646\n",
            "28:2019-10-31 16:58:05.038147\n",
            "29:2019-10-31 16:59:12.085974\n",
            "30:2019-10-31 17:00:19.074705\n",
            "31:2019-10-31 17:01:26.620020\n",
            "32:2019-10-31 17:02:35.133278\n",
            "34:2019-10-31 17:03:44.581933\n",
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            "36:2019-10-31 17:06:05.738871\n",
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            "38:2019-10-31 17:08:29.975709\n",
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            "42:2019-10-31 17:13:32.284985\n",
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            "81:2019-10-31 18:05:58.266395\n",
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            "97:2019-10-31 18:33:02.798553\n",
            "98:2019-10-31 18:34:57.537298\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ALM2izF7lQVs",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 85
        },
        "outputId": "8064c887-a300-40bd-bad1-6e597f43e21f"
      },
      "source": [
        "# Perform t-test on results (number of mislabels). \n",
        "\n",
        "fps = np.array(fps)\n",
        "statistic, pvalue = sp.stats.ttest_rel(fps[:,0], fps[:,1])\n",
        "\n",
        "print(np.mean(fps[:,0]))\n",
        "print(np.mean(fps[:,1]))\n",
        "\n",
        "print(statistic)\n",
        "print(pvalue)"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "6.666666666666667\n",
            "2.566666666666667\n",
            "7.77728080765712\n",
            "1.2412310150695e-11\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uIP-u94mpcWZ",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 85
        },
        "outputId": "2d31fa9c-4e54-4e63-dc88-9b241d7b9c82"
      },
      "source": [
        "# Perform t-test on errors\n",
        "\n",
        "accs = np.array(accs)\n",
        "statistic, pvalue = sp.stats.ttest_rel(1. - accs[:,0], 1. - accs[:,1])\n",
        "\n",
        "print(np.mean(1. - accs[:,0]))\n",
        "print(np.mean(1. - accs[:,1]))\n",
        "\n",
        "print(statistic)\n",
        "print(pvalue)"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "0.03553079364473858\n",
            "0.03625015871971373\n",
            "-2.608956344831146\n",
            "0.010652384228849258\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qWEL1WvxXMny",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 85
        },
        "outputId": "6c78afbc-4188-4441-e13e-46680ddaf35d"
      },
      "source": [
        "# Perform t-test on real world cost\n",
        "    \n",
        "fn_ws = np.array(ws)[:,0,:,:] # size (90, k, k)\n",
        "fp_ws = np.array(ws)[:,1,:,:] # size (90, k, k)\n",
        "\n",
        "preds_c = np.array(preds)[:,0,:,:] # size (90, k, k)\n",
        "preds_t = np.array(preds)[:,1,:,:] # size (90, k, k)\n",
        "\n",
        "costs_c = vector_categorical_real_world_cost(90, preds_c, fn_ws, fp_ws)\n",
        "costs_t = vector_categorical_real_world_cost(90, preds_t, fn_ws, fp_ws)\n",
        "\n",
        "assert costs_c.shape == (90,)\n",
        "assert costs_t.shape == (90,)\n",
        "\n",
        "print(np.mean(costs_c))\n",
        "print(np.mean(costs_t))\n",
        "\n",
        "statistic, pvalue = sp.stats.ttest_rel(costs_c, costs_t)\n",
        "print(statistic)\n",
        "print(pvalue)\n"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "0.042768888888888884\n",
            "0.039036825396825396\n",
            "5.983466153692239\n",
            "4.487857950902815e-08\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Pko_2OWPsnIG",
        "colab_type": "text"
      },
      "source": [
        "# Testing against imbalanced binary data\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lTjERIGrBzP9",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def create_imbalanced_mnist_data(X, y, target, num_minority, batch=0):\n",
        "  new_X, new_y = [], []\n",
        "  \n",
        "  mask = y == target\n",
        "  anti_mask = y != target\n",
        "\n",
        "  # Grab the target X\n",
        "  X_label = X[mask]  \n",
        "      \n",
        "  # Reduce the number of target x\n",
        "  start = batch * num_minority\n",
        "  end = start + num_minority\n",
        "  X_label = X_label[start:end,:]\n",
        "  \n",
        "  new_X = np.concatenate([X_label, X[anti_mask]])\n",
        "  new_y = np.concatenate([np.ones((num_minority)), np.zeros(X[anti_mask].shape[0])])\n",
        "  \n",
        "  return new_X, new_y\n",
        "\n",
        "def create_binary_model(loss):\n",
        "  k_y = k_x = Input(shape=(784,))\n",
        "  k_y = Dense(10, activation='relu')(k_y)\n",
        "  k_y = Dense(1, activation='sigmoid')(k_y)\n",
        "\n",
        "  model = Model(inputs=k_x, outputs=k_y)\n",
        "  model.compile(optimizer='adam', loss=loss, metrics=['binary_accuracy'])\n",
        "  return model\n",
        "\n",
        "def binary_real_world_cost(fn, fp, fn_cost, fp_cost):\n",
        "  return fn*fn_cost + fp*fp_cost\n",
        "\n",
        "def binary_stats(z, y, threshold, fn_cost, fp_cost):\n",
        "  z = np.squeeze(z)\n",
        "\n",
        "  y_pred = z > threshold\n",
        "  p = np.count_nonzero(y)\n",
        "  n = np.count_nonzero(1.-y)\n",
        "\n",
        "  tp = np.count_nonzero(y_pred * y)\n",
        "  fn = np.count_nonzero((1.-y_pred) * y)\n",
        "  tn = np.count_nonzero((1.-y_pred) * (1.-y))\n",
        "  fp = np.count_nonzero(y_pred * (1.-y))\n",
        "\n",
        "  recall = np.float64(tp) / (tp + fn) \n",
        "  precision = np.float64(tp) / (tp + fp)\n",
        "  f1 = np.float64(2 * recall * precision) / (recall + precision)\n",
        "  rwc = (binary_real_world_cost (fn, fp, fn_cost, fp_cost)) / (p+n)\n",
        "  rwb = (p * fn_cost) / (p+n) - rwc\n",
        "  err = (fn + fp) / n\n",
        "  \n",
        "  \n",
        "  # XXX: This really should return a dict instead of an 12 tuple. \n",
        "  return p, n, tp, fn, tn, fp, recall, precision, f1, rwc, rwb, err\n",
        "\n",
        "# This is the algorithm to fine tune the threshold hyperparameter after training. \n",
        "def search_threshold(z, y):\n",
        "  best_t = 0;\n",
        "  best_f1 = 0\n",
        "\n",
        "  data = []\n",
        "  \n",
        "  for i in np.linspace(0.01, .99, num=100):\n",
        "    _, _, _, _, _, _, _, _, f1, _, _, _ = binary_stats(z, y, i, 0, 0)\n",
        "    data.append((i, f1))\n",
        "    if f1 > best_f1:\n",
        "      best_f1 = f1\n",
        "      best_t = i  \n",
        "  return best_t, data"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YvoEA-TU_QMN",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 10518
        },
        "outputId": "1c8ced89-9673-452f-81f8-58aabf5db658"
      },
      "source": [
        "EPOCHS = 10 # We experimentally found no significant benefit after 10 epochs\n",
        "\n",
        "# For testing purposes only. Comment the following line out in typical usage. \n",
        "# EPOCHS = 1\n",
        "\n",
        "# Set some variables. \n",
        "FN_MARGINAL_COST = 2000 # E.g. if the disease is missed, it will get worse, costing an extra $2000 in future medical costs and pain and suffering\n",
        "FP_MARGINAL_COST = 100 # E.g. marginal cost of FP is the cost of running a second, more expensive test to identify the TN. \n",
        "\n",
        "stats = np.zeros((100,3,12))\n",
        "\n",
        "# Run it multiple times. \n",
        "for target in range (10):\n",
        "  for batch in range (10):\n",
        "    print(str(target) + \":\" + str(batch) + \":\" + str(datetime.datetime.now()))\n",
        "\n",
        "    #Processing on MNIST data\n",
        "    X = mnist.data.astype('float32')\n",
        "    y = mnist.target.astype('int64')\n",
        "    X /= 255.0\n",
        "\n",
        "    # Generate data. Return value is not randomized. \n",
        "    X, y = create_imbalanced_mnist_data(X, y, target, 630, batch)\n",
        "    # Shuffle and split into train and test data. \n",
        "    X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.25, random_state=1)\n",
        "\n",
        "    # Build control and test models. \n",
        "    model_control = create_binary_model('binary_crossentropy')\n",
        "    loss = create_rww_binary_crossentropy(FN_MARGINAL_COST, FP_MARGINAL_COST)\n",
        "    model_test = create_binary_model(loss)\n",
        "\n",
        "    model_control.fit(x = X_train, y = y_train, epochs=EPOCHS, batch_size=100, validation_split=0.1, verbose=0)      \n",
        "    model_test.fit(x = X_train, y = y_train, epochs=EPOCHS, batch_size=100, validation_split=0.1, verbose=0)  \n",
        "\n",
        "    y_pred_c = model_control.predict(X_test)\n",
        "    y_pred_t = model_test.predict(X_test)\n",
        "\n",
        "    stats_control = binary_stats(y_pred_c, y_test, 0.5, FN_MARGINAL_COST, FP_MARGINAL_COST)\n",
        "    best_threshold, data = search_threshold(y_pred_c, y_test)\n",
        "    stats_control_adj = binary_stats(y_pred_c, y_test, best_threshold, FN_MARGINAL_COST, FP_MARGINAL_COST)\n",
        "    stats_test = binary_stats(y_pred_t, y_test, 0.5, FN_MARGINAL_COST, FP_MARGINAL_COST)\n",
        "\n",
        "    print(tabulate([('Control',) + stats_control, \\\n",
        "                    ('Control_adj',) + stats_control_adj, \\\n",
        "                    ('Experimental',) + stats_test], \\\n",
        "                   headers=['P', 'N', 'TP', \"FN\", \"TN\", \"FP\", \"Recall\", \\\n",
        "                            \"Precision\", \"F1\", \"Real World Cost\", \\\n",
        "                            \"Real World Benefit\", \"Err\"], \\\n",
        "                   floatfmt=\".6f\"))\n",
        "\n",
        "    plt.plot(np.array(data)[:,0], np.array(data)[:,1])\n",
        "    plt.title('F1 Score by Threshhold')\n",
        "\n",
        "    stats[target * 10 + batch, 0] = stats_control\n",
        "    stats[target * 10 + batch, 1] = stats_control_adj\n",
        "    stats[target * 10 + batch, 2] = stats_test"
      ],
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "0:0:2019-10-31 18:36:52.181039\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       165  15767   143    22  15750    17  0.866667     0.893750  0.880000           2.868441             17.844590  0.002474\n",
            "Control_adj   165  15767   150    15  15743    24  0.909091     0.862069  0.884956           2.033643             18.679387  0.002474\n",
            "Experimental  165  15767   156     9  15722    45  0.945455     0.776119  0.852459           1.412252             19.300778  0.003425\n",
            "0:1:2019-10-31 18:38:34.587286\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       165  15767   153    12  15752    15  0.927273     0.910714  0.918919           1.600552             19.112478  0.001712\n",
            "Control_adj   165  15767   153    12  15752    15  0.927273     0.910714  0.918919           1.600552             19.112478  0.001712\n",
            "Experimental  165  15767   161     4  15684    83  0.975758     0.659836  0.787286           1.023098             19.689932  0.005518\n",
            "0:2:2019-10-31 18:40:18.017911\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/ipykernel_launcher.py:45: RuntimeWarning: invalid value encountered in double_scalars\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       165  15767   134    31  15764     3  0.812121     0.978102  0.887417           3.910369             16.802661  0.002156\n",
            "Control_adj   165  15767   151    14  15753    14  0.915152     0.915152  0.915152           1.845343             18.867688  0.001776\n",
            "Experimental  165  15767   156     9  15644   123  0.945455     0.559140  0.702703           1.901833             18.811198  0.008372\n",
            "0:3:2019-10-31 18:42:01.157101\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       165  15767   138    27  15761     6  0.836364     0.958333  0.893204           3.427065             17.285965  0.002093\n",
            "Control_adj   165  15767   149    16  15756    11  0.903030     0.931250  0.916923           2.077580             18.635451  0.001712\n",
            "Experimental  165  15767   158     7  15705    62  0.957576     0.718182  0.820779           1.267889             19.445142  0.004376\n",
            "0:4:2019-10-31 18:43:45.100448\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       165  15767   149    16  15759     8  0.903030     0.949045  0.925466           2.058750             18.654281  0.001522\n",
            "Control_adj   165  15767   153    12  15757    10  0.927273     0.938650  0.932927           1.569169             19.143861  0.001395\n",
            "Experimental  165  15767   159     6  15723    44  0.963636     0.783251  0.864130           1.029375             19.683656  0.003171\n",
            "0:5:2019-10-31 18:45:29.906822\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       165  15767   145    20  15763     4  0.878788     0.973154  0.923567           2.535777             18.177253  0.001522\n",
            "Control_adj   165  15767   145    20  15763     4  0.878788     0.973154  0.923567           2.535777             18.177253  0.001522\n",
            "Experimental  165  15767   161     4  15683    84  0.975758     0.657143  0.785366           1.029375             19.683656  0.005581\n",
            "0:6:2019-10-31 18:47:16.063064\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       165  15767   139    26  15761     6  0.842424     0.958621  0.896774           3.301532             17.411499  0.002030\n",
            "Control_adj   165  15767   146    19  15758     9  0.884848     0.941935  0.912500           2.441627             18.271403  0.001776\n",
            "Experimental  165  15767   160     5  15608   159  0.969697     0.501567  0.661157           1.625659             19.087371  0.010401\n",
            "0:7:2019-10-31 18:49:02.384246\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       165  15767   149    16  15750    17  0.903030     0.897590  0.900302           2.115240             18.597791  0.002093\n",
            "Control_adj   165  15767   144    21  15759     8  0.872727     0.947368  0.908517           2.686417             18.026613  0.001839\n",
            "Experimental  165  15767   158     7  15702    65  0.957576     0.708520  0.814433           1.286719             19.426312  0.004566\n",
            "0:8:2019-10-31 18:50:49.092097\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       165  15767   136    29  15761     6  0.824242     0.957746  0.885993           3.678132             17.034898  0.002220\n",
            "Control_adj   165  15767   143    22  15759     8  0.866667     0.947020  0.905063           2.811951             17.901080  0.001903\n",
            "Experimental  165  15767   154    11  15715    52  0.933333     0.747573  0.830189           1.707256             19.005775  0.003996\n",
            "0:9:2019-10-31 18:52:36.241140\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       165  15767   136    29  15755    12  0.824242     0.918919  0.869010           3.715792             16.997238  0.002600\n",
            "Control_adj   165  15767   147    18  15750    17  0.890909     0.896341  0.893617           2.366307             18.346724  0.002220\n",
            "Experimental  165  15767   156     9  15716    51  0.945455     0.753623  0.838710           1.449912             19.263118  0.003805\n",
            "1:0:2019-10-31 18:54:25.198525\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       165  15524   154    11  15513    11  0.933333     0.933333  0.933333           1.472369             19.561476  0.001417\n",
            "Control_adj   165  15524   154    11  15518     6  0.933333     0.962500  0.947692           1.440500             19.593346  0.001095\n",
            "Experimental  165  15524   157     8  15477    47  0.951515     0.769608  0.850949           1.319396             19.714450  0.003543\n",
            "1:1:2019-10-31 18:56:13.281891\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       165  15524   152    13  15509    15  0.921212     0.910180  0.915663           1.752820             19.281025  0.001804\n",
            "Control_adj   165  15524   152    13  15514    10  0.921212     0.938272  0.929664           1.720951             19.312894  0.001482\n",
            "Experimental  165  15524   156     9  15474    50  0.945455     0.757282  0.840970           1.465995             19.567850  0.003801\n",
            "1:2:2019-10-31 18:58:02.159415\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       165  15524   140    25  15516     8  0.848485     0.945946  0.894569           3.237937             17.795908  0.002126\n",
            "Control_adj   165  15524   146    19  15511    13  0.884848     0.918239  0.901235           2.504940             18.528906  0.002061\n",
            "Experimental  165  15524   154    11  15475    49  0.933333     0.758621  0.836957           1.714577             19.319268  0.003865\n",
            "1:3:2019-10-31 18:59:50.596275\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       165  15524   149    16  15514    10  0.903030     0.937107  0.919753           2.103385             18.930461  0.001675\n",
            "Control_adj   165  15524   149    16  15514    10  0.903030     0.937107  0.919753           2.103385             18.930461  0.001675\n",
            "Experimental  165  15524   151    14  15483    41  0.915152     0.786458  0.845938           2.046020             18.987826  0.003543\n",
            "1:4:2019-10-31 19:01:40.074504\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       165  15524   144    21  15515     9  0.872727     0.941176  0.905660           2.734400             18.299445  0.001932\n",
            "Control_adj   165  15524   143    22  15521     3  0.866667     0.979452  0.919614           2.823634             18.210211  0.001610\n",
            "Experimental  165  15524   158     7  15449    75  0.957576     0.678112  0.793970           1.370387             19.663458  0.005282\n",
            "1:5:2019-10-31 19:03:30.068145\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       165  15524   152    13  15510    14  0.921212     0.915663  0.918429           1.746447             19.287399  0.001739\n",
            "Control_adj   165  15524   149    16  15520     4  0.903030     0.973856  0.937107           2.065141             18.968704  0.001288\n",
            "Experimental  165  15524   159     6  15469    55  0.963636     0.742991  0.839050           1.115431             19.918414  0.003929\n",
            "1:6:2019-10-31 19:05:21.425402\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       165  15524   156     9  15510    14  0.945455     0.917647  0.931343           1.236535             19.797310  0.001482\n",
            "Control_adj   165  15524   152    13  15519     5  0.921212     0.968153  0.944099           1.689082             19.344764  0.001159\n",
            "Experimental  165  15524   162     3  15438    86  0.981818     0.653226  0.784504           0.930588             20.103257  0.005733\n",
            "1:7:2019-10-31 19:07:12.754722\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       165  15524   155    10  15516     8  0.939394     0.950920  0.945122           1.325770             19.708076  0.001159\n",
            "Control_adj   165  15524   153    12  15522     2  0.927273     0.987097  0.956250           1.542482             19.491363  0.000902\n",
            "Experimental  165  15524   159     6  15473    51  0.963636     0.757143  0.848000           1.089936             19.943910  0.003672\n",
            "1:8:2019-10-31 19:09:05.169757\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       165  15524   146    19  15514    10  0.884848     0.935897  0.909657           2.485818             18.548027  0.001868\n",
            "Control_adj   165  15524   149    16  15513    11  0.903030     0.931250  0.916923           2.109758             18.924087  0.001739\n",
            "Experimental  165  15524   159     6  15476    48  0.963636     0.768116  0.854839           1.070814             19.963031  0.003478\n",
            "1:9:2019-10-31 19:10:56.649888\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       165  15524   153    12  15508    16  0.927273     0.905325  0.916168           1.631716             19.402129  0.001804\n",
            "Control_adj   165  15524   152    13  15514    10  0.921212     0.938272  0.929664           1.720951             19.312894  0.001482\n",
            "Experimental  165  15524   162     3  15481    43  0.981818     0.790244  0.875676           0.656511             20.377334  0.002963\n",
            "2:0:2019-10-31 19:12:48.571538\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       164  15746   111    53  15737     9  0.676829     0.925000  0.781690           6.719045             13.896920  0.003938\n",
            "Control_adj   164  15746   123    41  15735    11  0.750000     0.917910  0.825503           5.223130             15.392835  0.003302\n",
            "Experimental  164  15746   144    20  15673    73  0.878049     0.663594  0.755906           2.972973             17.642992  0.005906\n",
            "2:1:2019-10-31 19:14:42.256059\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       164  15746   110    54  15739     7  0.670732     0.940171  0.782918           6.832181             13.783784  0.003874\n",
            "Control_adj   164  15746   126    38  15736    10  0.768293     0.926471  0.840000           4.839723             15.776241  0.003048\n",
            "Experimental  164  15746   145    19  15657    89  0.884146     0.619658  0.728643           2.947832             17.668133  0.006859\n",
            "2:2:2019-10-31 19:16:36.715873\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       164  15746   114    50  15739     7  0.695122     0.942149  0.800000           6.329353             14.286612  0.003620\n",
            "Control_adj   164  15746   139    25  15713    33  0.847561     0.808140  0.827381           3.350094             17.265871  0.003683\n",
            "Experimental  164  15746   152    12  15675    71  0.926829     0.681614  0.785530           1.954745             18.661219  0.005271\n",
            "2:3:2019-10-31 19:18:32.030035\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       164  15746   128    36  15728    18  0.780488     0.876712  0.825806           4.638592             15.977373  0.003429\n",
            "Control_adj   164  15746   135    29  15726    20  0.823171     0.870968  0.846395           3.771213             16.844752  0.003112\n",
            "Experimental  164  15746   146    18  15664    82  0.890244     0.640351  0.744898           2.778127             17.837838  0.006351\n",
            "2:4:2019-10-31 19:20:28.206184\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       164  15746   132    32  15728    18  0.804878     0.880000  0.840764           4.135764             16.480201  0.003175\n",
            "Control_adj   164  15746   139    25  15725    21  0.847561     0.868750  0.858025           3.274670             17.341295  0.002921\n",
            "Experimental  164  15746   146    18  15622   124  0.890244     0.540741  0.672811           3.042112             17.573853  0.009018\n",
            "2:5:2019-10-31 19:22:24.235727\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       164  15746   123    41  15735    11  0.750000     0.917910  0.825503           5.223130             15.392835  0.003302\n",
            "Control_adj   164  15746   140    24  15724    22  0.853659     0.864198  0.858896           3.155248             17.460717  0.002921\n",
            "Experimental  164  15746   151    13  15661    85  0.920732     0.639831  0.755000           2.168448             18.447517  0.006224\n",
            "2:6:2019-10-31 19:24:22.019438\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       164  15746   117    47  15744     2  0.713415     0.983193  0.826855           5.920805             14.695160  0.003112\n",
            "Control_adj   164  15746   131    33  15735    11  0.798780     0.922535  0.856209           4.217473             16.398492  0.002794\n",
            "Experimental  164  15746   151    13  15611   135  0.920732     0.527972  0.671111           2.482715             18.133250  0.009399\n",
            "2:7:2019-10-31 19:26:19.362033\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       164  15746   128    36  15732    14  0.780488     0.901408  0.836601           4.613451             16.002514  0.003175\n",
            "Control_adj   164  15746   133    31  15729    17  0.810976     0.886667  0.847134           4.003771             16.612194  0.003048\n",
            "Experimental  164  15746   139    25  15657    89  0.847561     0.609649  0.709184           3.702074             16.913891  0.007240\n",
            "2:8:2019-10-31 19:28:17.773405\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       164  15746   129    35  15728    18  0.786585     0.877551  0.829582           4.512885             16.103080  0.003366\n",
            "Control_adj   164  15746   129    35  15730    16  0.786585     0.889655  0.834951           4.500314             16.115651  0.003239\n",
            "Experimental  164  15746   145    19  15608   138  0.884146     0.512367  0.648770           3.255814             17.360151  0.009971\n",
            "2:9:2019-10-31 19:30:17.495907\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       164  15746   140    24  15730    16  0.853659     0.897436  0.875000           3.117536             17.498429  0.002540\n",
            "Control_adj   164  15746   143    21  15727    19  0.871951     0.882716  0.877301           2.759271             17.856694  0.002540\n",
            "Experimental  164  15746   149    15  15617   129  0.908537     0.535971  0.674208           2.696417             17.919547  0.009145\n",
            "3:0:2019-10-31 19:32:17.555691\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       163  15710   117    46  15691    19  0.717791     0.860294  0.782609           5.915706             14.622315  0.004137\n",
            "Control_adj   163  15710   125    38  15685    25  0.766871     0.833333  0.798722           4.945505             15.592516  0.004010\n",
            "Experimental  163  15710   145    18  15567   143  0.889571     0.503472  0.643016           3.168903             17.369117  0.010248\n",
            "3:1:2019-10-31 19:34:18.407651\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       163  15710    97    66  15705     5  0.595092     0.950980  0.732075           8.347508             12.190512  0.004519\n",
            "Control_adj   163  15710   117    46  15694    16  0.717791     0.879699  0.790541           5.896806             14.641215  0.003947\n",
            "Experimental  163  15710   141    22  15500   210  0.865031     0.401709  0.548638           4.095004             16.443016  0.014768\n",
            "3:2:2019-10-31 19:36:19.398641\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       163  15710   114    49  15699    11  0.699387     0.912000  0.791667           6.243306             14.294714  0.003819\n",
            "Control_adj   163  15710   125    38  15688    22  0.766871     0.850340  0.806452           4.926605             15.611416  0.003819\n",
            "Experimental  163  15710   134    29  15569   141  0.822086     0.487273  0.611872           4.542305             15.995716  0.010821\n",
            "3:3:2019-10-31 19:38:21.385260\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       163  15710   123    40  15693    17  0.754601     0.878571  0.811881           5.147105             15.390915  0.003628\n",
            "Control_adj   163  15710   140    23  15678    32  0.858896     0.813953  0.835821           3.099603             17.438417  0.003501\n",
            "Experimental  163  15710   153    10  15488   222  0.938650     0.408000  0.568773           2.658603             17.879418  0.014768\n",
            "3:4:2019-10-31 19:40:24.103779\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       163  15710   107    56  15698    12  0.656442     0.899160  0.758865           7.131607             13.406413  0.004328\n",
            "Control_adj   163  15710   115    48  15696    14  0.705521     0.891473  0.787671           6.136206             14.401814  0.003947\n",
            "Experimental  163  15710   131    32  15599   111  0.803681     0.541322  0.646914           4.731305             15.806716  0.009102\n",
            "3:5:2019-10-31 19:42:27.479713\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       163  15710   115    48  15685    25  0.705521     0.821429  0.759076           6.205506             14.332514  0.004647\n",
            "Control_adj   163  15710   115    48  15686    24  0.705521     0.827338  0.761589           6.199206             14.338814  0.004583\n",
            "Experimental  163  15710   139    24  15587   123  0.852761     0.530534  0.654118           3.798904             16.739117  0.009357\n",
            "3:6:2019-10-31 19:44:31.531240\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       163  15710   114    49  15697    13  0.699387     0.897638  0.786207           6.255906             14.282114  0.003947\n",
            "Control_adj   163  15710   124    39  15689    21  0.760736     0.855172  0.805195           5.046305             15.491715  0.003819\n",
            "Experimental  163  15710   132    31  15588   122  0.809816     0.519685  0.633094           4.674605             15.863416  0.009739\n",
            "3:7:2019-10-31 19:46:36.730179\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       163  15710   109    54  15698    12  0.668712     0.900826  0.767606           6.879607             13.658414  0.004201\n",
            "Control_adj   163  15710   121    42  15684    26  0.742331     0.823129  0.780645           5.455805             15.082215  0.004328\n",
            "Experimental  163  15710   141    22  15507   203  0.865031     0.409884  0.556213           4.050904             16.487116  0.014322\n",
            "3:8:2019-10-31 19:48:40.775505\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       163  15710   122    41  15689    21  0.748466     0.853147  0.797386           5.298305             15.239715  0.003947\n",
            "Control_adj   163  15710   121    42  15697    13  0.742331     0.902985  0.814815           5.373905             15.164115  0.003501\n",
            "Experimental  163  15710   139    24  15522   188  0.852761     0.425076  0.567347           4.208404             16.329616  0.013495\n",
            "3:9:2019-10-31 19:50:46.097552\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       163  15710   120    43  15698    12  0.736196     0.909091  0.813559           5.493605             15.044415  0.003501\n",
            "Control_adj   163  15710   129    34  15689    21  0.791411     0.860000  0.824281           4.416304             16.121716  0.003501\n",
            "Experimental  163  15710   143    20  15571   139  0.877301     0.507092  0.642697           3.395703             17.142317  0.010121\n",
            "4:0:2019-10-31 19:52:51.417832\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       167  15785   128    39  15771    14  0.766467     0.901408  0.828479           4.977432             15.960381  0.003358\n",
            "Control_adj   167  15785   128    39  15773    12  0.766467     0.914286  0.833876           4.964895             15.972919  0.003231\n",
            "Experimental  167  15785   161     6  15564   221  0.964072     0.421466  0.586521           2.137663             18.800150  0.014381\n",
            "4:1:2019-10-31 19:54:58.795323\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       167  15785   136    31  15766    19  0.814371     0.877419  0.844720           4.005767             16.932046  0.003168\n",
            "Control_adj   167  15785   144    23  15760    25  0.862275     0.852071  0.857143           3.040371             17.897442  0.003041\n",
            "Experimental  167  15785   154    13  15710    75  0.922156     0.672489  0.777778           2.100050             18.837763  0.005575\n",
            "4:2:2019-10-31 19:57:06.847310\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       167  15785   132    35  15761    24  0.790419     0.846154  0.817337           4.538616             16.399198  0.003738\n",
            "Control_adj   167  15785   130    37  15767    18  0.778443     0.878378  0.825397           4.751755             16.186058  0.003484\n",
            "Experimental  167  15785   154    13  15613   172  0.922156     0.472393  0.624746           2.708124             18.229689  0.011720\n",
            "4:3:2019-10-31 19:59:15.078341\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       167  15785    98    69  15778     7  0.586826     0.933333  0.720588           8.694835             12.242979  0.004815\n",
            "Control_adj   167  15785   130    37  15756    29  0.778443     0.817610  0.797546           4.820712             16.117101  0.004181\n",
            "Experimental  167  15785   155    12  15633   152  0.928144     0.504886  0.654008           2.457372             18.480441  0.010390\n",
            "4:4:2019-10-31 20:01:22.782420\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       167  15785   143    24  15762    23  0.856287     0.861446  0.858859           3.153210             17.784604  0.002978\n",
            "Control_adj   167  15785   146    21  15759    26  0.874251     0.848837  0.861357           2.795888             18.141926  0.002978\n",
            "Experimental  167  15785   152    15  15675   110  0.910180     0.580153  0.708625           2.570211             18.367603  0.007919\n",
            "4:5:2019-10-31 20:03:32.723995\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       167  15785   132    35  15770    15  0.790419     0.897959  0.840764           4.482197             16.455617  0.003168\n",
            "Control_adj   167  15785   136    31  15767    18  0.814371     0.883117  0.847352           3.999498             16.938315  0.003104\n",
            "Experimental  167  15785   157    10  15686    99  0.940120     0.613281  0.742317           1.874373             19.063440  0.006905\n",
            "4:6:2019-10-31 20:05:43.049432\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       167  15785   132    35  15773    12  0.790419     0.916667  0.848875           4.463390             16.474423  0.002978\n",
            "Control_adj   167  15785   139    28  15770    15  0.832335     0.902597  0.866044           3.604564             17.333250  0.002724\n",
            "Experimental  167  15785   150    17  15671   114  0.898204     0.568182  0.696056           2.846038             18.091775  0.008299\n",
            "4:7:2019-10-31 20:07:53.482164\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       167  15785   120    47  15774    11  0.718563     0.916031  0.805369           5.961635             14.976179  0.003674\n",
            "Control_adj   167  15785   120    47  15774    11  0.718563     0.916031  0.805369           5.961635             14.976179  0.003674\n",
            "Experimental  167  15785   145    22  15682   103  0.868263     0.584677  0.698795           3.403962             17.533852  0.007919\n",
            "4:8:2019-10-31 20:10:03.561039\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       167  15785   131    36  15764    21  0.784431     0.861842  0.821317           4.645186             16.292628  0.003611\n",
            "Control_adj   167  15785   143    24  15758    27  0.856287     0.841176  0.848665           3.178285             17.759529  0.003231\n",
            "Experimental  167  15785   161     6  15623   162  0.964072     0.498452  0.657143           1.767803             19.170010  0.010643\n",
            "4:9:2019-10-31 20:12:15.215988\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       167  15785   139    28  15772    13  0.832335     0.914474  0.871473           3.592026             17.345787  0.002597\n",
            "Control_adj   167  15785   137    30  15779     6  0.820359     0.958042  0.883871           3.798897             17.138917  0.002281\n",
            "Experimental  167  15785   155    12  15655   130  0.928144     0.543860  0.685841           2.319458             18.618355  0.008996\n",
            "5:0:2019-10-31 20:14:26.591118\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       165  15915   112    53  15906     9  0.678788     0.925620  0.783217           6.648010             13.874378  0.003896\n",
            "Control_adj   165  15915   130    35  15894    21  0.787879     0.860927  0.822785           4.483831             16.038557  0.003519\n",
            "Experimental  165  15915   148    17  15836    79  0.896970     0.651982  0.755102           2.605721             17.916667  0.006032\n",
            "5:1:2019-10-31 20:16:39.600098\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       165  15915    94    71  15904    11  0.569697     0.895238  0.696296           8.899254             11.623134  0.005152\n",
            "Control_adj   165  15915   129    36  15880    35  0.781818     0.786585  0.784195           4.695274             15.827114  0.004461\n",
            "Experimental  165  15915   138    27  15660   255  0.836364     0.351145  0.494624           4.944030             15.578358  0.017719\n",
            "5:2:2019-10-31 20:18:52.936835\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       165  15915    98    67  15903    12  0.593939     0.890909  0.712727           8.407960             12.114428  0.004964\n",
            "Control_adj   165  15915   110    55  15885    30  0.666667     0.785714  0.721311           7.027363             13.495025  0.005341\n",
            "Experimental  165  15915   132    33  15857    58  0.800000     0.694737  0.743662           4.465174             16.057214  0.005718\n",
            "5:3:2019-10-31 20:21:06.876155\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       165  15915   117    48  15907     8  0.709091     0.936000  0.806897           6.019900             14.502488  0.003519\n",
            "Control_adj   165  15915   129    36  15899    16  0.781818     0.889655  0.832258           4.577114             15.945274  0.003267\n",
            "Experimental  165  15915   142    23  15843    72  0.860606     0.663551  0.749340           3.308458             17.213930  0.005969\n",
            "5:4:2019-10-31 20:23:21.242277\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       165  15915   110    55  15901    14  0.666667     0.887097  0.761246           6.927861             13.594527  0.004336\n",
            "Control_adj   165  15915   119    46  15894    21  0.721212     0.850000  0.780328           5.851990             14.670398  0.004210\n",
            "Experimental  165  15915   147    18  15795   120  0.890909     0.550562  0.680556           2.985075             17.537313  0.008671\n",
            "5:5:2019-10-31 20:25:36.574102\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       165  15915    96    69  15902    13  0.581818     0.880734  0.700730           8.662935             11.859453  0.005152\n",
            "Control_adj   165  15915   119    46  15893    22  0.721212     0.843972  0.777778           5.858209             14.664179  0.004273\n",
            "Experimental  165  15915   134    31  15792   123  0.812121     0.521401  0.635071           4.620647             15.901741  0.009676\n",
            "5:6:2019-10-31 20:27:52.956820\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       165  15915   126    39  15899    16  0.763636     0.887324  0.820847           4.950249             15.572139  0.003456\n",
            "Control_adj   165  15915   131    34  15898    17  0.793939     0.885135  0.837061           4.334577             16.187811  0.003205\n",
            "Experimental  165  15915   148    17  15849    66  0.896970     0.691589  0.781003           2.524876             17.997512  0.005215\n",
            "5:7:2019-10-31 20:30:09.278681\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       165  15915    93    72  15907     8  0.563636     0.920792  0.699248           9.004975             11.517413  0.005027\n",
            "Control_adj   165  15915   127    38  15870    45  0.769697     0.738372  0.753709           5.006219             15.516169  0.005215\n",
            "Experimental  165  15915   143    22  15708   207  0.866667     0.408571  0.555340           4.023632             16.498756  0.014389\n",
            "5:8:2019-10-31 20:32:26.182906\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       165  15915   118    47  15893    22  0.715152     0.842857  0.773770           5.982587             14.539801  0.004336\n",
            "Control_adj   165  15915   132    33  15884    31  0.800000     0.809816  0.804878           4.297264             16.225124  0.004021\n",
            "Experimental  165  15915   140    25  15824    91  0.848485     0.606061  0.707071           3.675373             16.847015  0.007289\n",
            "5:9:2019-10-31 20:34:43.905358\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       165  15915   116    49  15908     7  0.703030     0.943089  0.805556           6.138060             14.384328  0.003519\n",
            "Control_adj   165  15915   129    36  15902    13  0.781818     0.908451  0.840391           4.558458             15.963930  0.003079\n",
            "Experimental  165  15915   141    24  15868    47  0.854545     0.750000  0.798867           3.277363             17.245025  0.004461\n",
            "6:0:2019-10-31 20:37:01.075317\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       165  15774   140    25  15763    11  0.848485     0.927152  0.886076           3.205973             17.497961  0.002282\n",
            "Control_adj   165  15774   144    21  15762    12  0.872727     0.923077  0.897196           2.710333             17.993601  0.002092\n",
            "Experimental  165  15774   158     7  15636   138  0.957576     0.533784  0.685466           1.744150             18.959784  0.009192\n",
            "6:1:2019-10-31 20:39:18.784788\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       165  15774   153    12  15752    22  0.927273     0.874286  0.900000           1.643767             19.060167  0.002155\n",
            "Control_adj   165  15774   149    16  15769     5  0.903030     0.967532  0.934169           2.039024             18.664910  0.001331\n",
            "Experimental  165  15774   156     9  15591   183  0.945455     0.460177  0.619048           2.277433             18.426501  0.012172\n",
            "6:2:2019-10-31 20:41:39.437252\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       165  15774   136    29  15747    27  0.824242     0.834356  0.829268           3.808269             16.895665  0.003550\n",
            "Control_adj   165  15774   138    27  15747    27  0.836364     0.836364  0.836364           3.557312             17.146621  0.003423\n",
            "Experimental  165  15774   149    16  15691    83  0.903030     0.642241  0.750630           2.528389             18.175544  0.006276\n",
            "6:3:2019-10-31 20:43:56.971191\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       165  15774   138    27  15763    11  0.836364     0.926174  0.878981           3.456930             17.247004  0.002409\n",
            "Control_adj   165  15774   145    20  15759    15  0.878788     0.906250  0.892308           2.603677             18.100257  0.002219\n",
            "Experimental  165  15774   156     9  15663   111  0.945455     0.584270  0.722222           1.825711             18.878223  0.007607\n",
            "6:4:2019-10-31 20:46:14.013848\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       165  15774   133    32  15757    17  0.806061     0.886667  0.844444           4.121965             16.581969  0.003106\n",
            "Control_adj   165  15774   138    27  15754    20  0.836364     0.873418  0.854489           3.513395             17.190539  0.002980\n",
            "Experimental  165  15774   158     7  15612   162  0.957576     0.493750  0.651546           1.894724             18.809210  0.010714\n",
            "6:5:2019-10-31 20:48:33.066824\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       165  15774   136    29  15743    31  0.824242     0.814371  0.819277           3.833365             16.870569  0.003804\n",
            "Control_adj   165  15774   135    30  15747    27  0.818182     0.833333  0.825688           3.933747             16.770186  0.003614\n",
            "Experimental  165  15774   143    22  15670   104  0.866667     0.578947  0.694175           3.413012             17.290922  0.007988\n",
            "6:6:2019-10-31 20:50:52.959730\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       165  15774   132    33  15764    10  0.800000     0.929577  0.859935           4.203526             16.500408  0.002726\n",
            "Control_adj   165  15774   138    27  15761    13  0.836364     0.913907  0.873418           3.469477             17.234456  0.002536\n",
            "Experimental  165  15774   152    13  15713    61  0.921212     0.713615  0.804233           2.013928             18.690006  0.004691\n",
            "6:7:2019-10-31 20:53:13.215703\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       165  15774   144    21  15743    31  0.872727     0.822857  0.847059           2.829538             17.874396  0.003297\n",
            "Control_adj   165  15774   138    27  15758    16  0.836364     0.896104  0.865204           3.488299             17.215635  0.002726\n",
            "Experimental  165  15774   158     7  15554   220  0.957576     0.417989  0.581952           2.258611             18.445323  0.014391\n",
            "6:8:2019-10-31 20:55:33.305889\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       165  15774   143    22  15762    12  0.866667     0.922581  0.893750           2.835812             17.868122  0.002155\n",
            "Control_adj   165  15774   142    23  15768     6  0.860606     0.959459  0.907348           2.923646             17.780287  0.001838\n",
            "Experimental  165  15774   152    13  15702    72  0.921212     0.678571  0.781491           2.082941             18.620993  0.005389\n",
            "6:9:2019-10-31 20:57:56.457661\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       165  15774   137    28  15762    12  0.830303     0.919463  0.872611           3.588682             17.115252  0.002536\n",
            "Control_adj   165  15774   137    28  15765     9  0.830303     0.938356  0.881029           3.569860             17.134074  0.002346\n",
            "Experimental  165  15774   151    14  15703    71  0.915152     0.680180  0.780362           2.202146             18.501788  0.005389\n",
            "7:0:2019-10-31 21:00:20.297221\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       161  15674   135    26  15654    20  0.838509     0.870968  0.854430           3.410167             16.924534  0.002935\n",
            "Control_adj   161  15674   135    26  15655    19  0.838509     0.876623  0.857143           3.403852             16.930849  0.002871\n",
            "Experimental  161  15674   142    19  15619    55  0.881988     0.720812  0.793296           2.747079             17.587622  0.004721\n",
            "7:1:2019-10-31 21:02:43.262305\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       161  15674   129    32  15651    23  0.801242     0.848684  0.824281           4.186928             16.147774  0.003509\n",
            "Control_adj   161  15674   128    33  15655    19  0.795031     0.870748  0.831169           4.287970             16.046732  0.003318\n",
            "Experimental  161  15674   155     6  15504   170  0.962733     0.476923  0.637860           1.831386             18.503315  0.011229\n",
            "7:2:2019-10-31 21:05:07.722683\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       161  15674   131    30  15658    16  0.813665     0.891156  0.850649           3.890117             16.444585  0.002935\n",
            "Control_adj   161  15674   140    21  15651    23  0.869565     0.858896  0.864198           2.797600             17.537101  0.002807\n",
            "Experimental  161  15674   153     8  15581    93  0.950311     0.621951  0.751843           1.597727             18.736975  0.006444\n",
            "7:3:2019-10-31 21:07:34.231129\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       161  15674   127    34  15662    12  0.788820     0.913669  0.846667           4.370066             15.964635  0.002935\n",
            "Control_adj   161  15674   136    25  15652    22  0.844720     0.860759  0.852665           3.296495             17.038207  0.002999\n",
            "Experimental  161  15674   150    11  15588    86  0.931677     0.635593  0.755668           1.932428             18.402273  0.006189\n",
            "7:4:2019-10-31 21:10:02.331091\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       161  15674   130    31  15660    14  0.807453     0.902778  0.852459           4.003789             16.330913  0.002871\n",
            "Control_adj   161  15674   130    31  15660    14  0.807453     0.902778  0.852459           4.003789             16.330913  0.002871\n",
            "Experimental  161  15674   147    14  15616    58  0.913043     0.717073  0.803279           2.134512             18.200189  0.004594\n",
            "7:5:2019-10-31 21:12:30.196806\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       161  15674   134    27  15653    21  0.832298     0.864516  0.848101           3.542785             16.791917  0.003062\n",
            "Control_adj   161  15674   138    23  15652    22  0.857143     0.862500  0.859813           3.043890             17.290811  0.002871\n",
            "Experimental  161  15674   150    11  15581    93  0.931677     0.617284  0.742574           1.976634             18.358068  0.006635\n",
            "7:6:2019-10-31 21:14:58.064563\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       161  15674   128    33  15661    13  0.795031     0.907801  0.847682           4.250079             16.084623  0.002935\n",
            "Control_adj   161  15674   141    20  15653    21  0.875776     0.870370  0.873065           2.658668             17.676034  0.002616\n",
            "Experimental  161  15674   144    17  15490   184  0.894410     0.439024  0.588957           3.309125             17.025576  0.012824\n",
            "7:7:2019-10-31 21:17:28.584254\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       161  15674   108    53  15667     7  0.670807     0.939130  0.782609           6.738238             13.596464  0.003828\n",
            "Control_adj   161  15674   132    29  15657    17  0.819876     0.885906  0.851613           3.770129             16.564572  0.002935\n",
            "Experimental  161  15674   147    14  15616    58  0.913043     0.717073  0.803279           2.134512             18.200189  0.004594\n",
            "7:8:2019-10-31 21:19:59.551216\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       161  15674   123    38  15661    13  0.763975     0.904412  0.828283           4.881591             15.453110  0.003254\n",
            "Control_adj   161  15674   134    27  15652    22  0.832298     0.858974  0.845426           3.549100             16.785602  0.003126\n",
            "Experimental  161  15674   151    10  15600    74  0.937888     0.671111  0.782383           1.730344             18.604357  0.005359\n",
            "7:9:2019-10-31 21:22:30.506319\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       161  15674   136    25  15657    17  0.844720     0.888889  0.866242           3.264919             17.069782  0.002680\n",
            "Control_adj   161  15674   136    25  15657    17  0.844720     0.888889  0.866242           3.264919             17.069782  0.002680\n",
            "Experimental  161  15674   147    14  15556   118  0.913043     0.554717  0.690141           2.513420             17.821282  0.008422\n",
            "8:0:2019-10-31 21:24:58.997794\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       167  15785    82    85  15782     3  0.491018     0.964706  0.650794          10.675777             10.262036  0.005575\n",
            "Control_adj   167  15785   130    37  15769    16  0.778443     0.890411  0.830671           4.739218             16.198596  0.003358\n",
            "Experimental  167  15785   148    19  15601   184  0.886228     0.445783  0.593186           3.535607             17.402207  0.012860\n",
            "8:1:2019-10-31 21:27:28.829725\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       167  15785    88    79  15782     3  0.526946     0.967033  0.682171           9.923521             11.014293  0.005195\n",
            "Control_adj   167  15785   136    31  15747    38  0.814371     0.781609  0.797654           4.124875             16.812939  0.004371\n",
            "Experimental  167  15785   148    19  15588   197  0.886228     0.428986  0.578125           3.617101             17.320712  0.013684\n",
            "8:2:2019-10-31 21:30:00.258618\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       167  15785   102    65  15777     8  0.610778     0.927273  0.736462           8.199599             12.738215  0.004625\n",
            "Control_adj   167  15785   140    27  15753    32  0.838323     0.813953  0.825959           3.585757             17.352056  0.003738\n",
            "Experimental  167  15785   148    19  15639   146  0.886228     0.503401  0.642082           3.297392             17.640421  0.010453\n",
            "8:3:2019-10-31 21:32:32.304298\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       167  15785    79    88  15780     5  0.473054     0.940476  0.629482          11.064443              9.873370  0.005892\n",
            "Control_adj   167  15785   107    60  15767    18  0.640719     0.856000  0.732877           7.635406             13.302407  0.004941\n",
            "Experimental  167  15785   129    38  15681   104  0.772455     0.553648  0.645000           5.416249             15.521565  0.008996\n",
            "8:4:2019-10-31 21:35:06.122409\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision          F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  ----------  -----------------  --------------------  --------\n",
            "Control       167  15785     0   167  15785     0  0.000000   nan         nan                 20.937813              0.000000  0.010580\n",
            "Control_adj   167  15785   118    49  15736    49  0.706587     0.706587    0.706587           6.450602             14.487212  0.006208\n",
            "Experimental  167  15785   144    23  15605   180  0.862275     0.444444    0.586558           4.012036             16.925777  0.012860\n",
            "8:5:2019-10-31 21:37:37.849062\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       167  15785    78    89  15783     2  0.467066     0.975000  0.631579          11.171013              9.766800  0.005765\n",
            "Control_adj   167  15785   115    52  15772    13  0.688623     0.898438  0.779661           6.601053             14.336760  0.004118\n",
            "Experimental  167  15785   142    25  15451   334  0.850299     0.298319  0.441680           5.228185             15.709629  0.022743\n",
            "8:6:2019-10-31 21:40:11.222352\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       167  15785    81    86  15781     4  0.485030     0.952941  0.642857          10.807422             10.130391  0.005702\n",
            "Control_adj   167  15785   119    48  15754    31  0.712575     0.793333  0.750789           6.212387             14.725426  0.005005\n",
            "Experimental  167  15785   140    27  15484   301  0.838323     0.317460  0.460526           5.272066             15.665747  0.020779\n",
            "8:7:2019-10-31 21:42:45.256649\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       167  15785    80    87  15779     6  0.479042     0.930233  0.632411          10.945336              9.992477  0.005892\n",
            "Control_adj   167  15785   123    44  15747    38  0.736527     0.763975  0.750000           5.754764             15.183049  0.005195\n",
            "Experimental  167  15785   151    16  15362   423  0.904192     0.263066  0.407557           4.657723             16.280090  0.027811\n",
            "8:8:2019-10-31 21:45:19.288035\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       167  15785   110    57  15768    17  0.658683     0.866142  0.748299           7.253009             13.684804  0.004688\n",
            "Control_adj   167  15785   122    45  15755    30  0.730539     0.802632  0.764890           5.829990             15.107823  0.004751\n",
            "Experimental  167  15785   140    27  15656   129  0.838323     0.520446  0.642202           4.193831             16.743982  0.009883\n",
            "8:9:2019-10-31 21:47:53.735902\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       167  15785    94    73  15780     5  0.562874     0.949495  0.706767           9.183801             11.754012  0.004941\n",
            "Control_adj   167  15785   115    52  15768    17  0.688623     0.871212  0.769231           6.626128             14.311685  0.004371\n",
            "Experimental  167  15785   145    22  15685   100  0.868263     0.591837  0.703883           3.385155             17.552658  0.007729\n",
            "9:0:2019-10-31 21:50:28.731063\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       165  15753    79    86  15740    13  0.478788     0.858696  0.614786          10.887046              9.844202  0.006285\n",
            "Control_adj   165  15753   112    53  15710    43  0.678788     0.722581  0.700000           6.929262             13.801985  0.006094\n",
            "Experimental  165  15753   145    20  15564   189  0.878788     0.434132  0.581162           3.700214             17.031034  0.013267\n",
            "9:1:2019-10-31 21:53:04.279797\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       165  15753   101    64  15743    10  0.612121     0.909910  0.731884           8.104033             12.627214  0.004698\n",
            "Control_adj   165  15753   122    43  15721    32  0.739394     0.792208  0.764890           5.603719             15.127529  0.004761\n",
            "Experimental  165  15753   149    16  15553   200  0.903030     0.426934  0.579767           3.266742             17.464506  0.013712\n",
            "9:2:2019-10-31 21:55:39.428174\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       165  15753    96    69  15742    11  0.581818     0.897196  0.705882           8.738535             11.992713  0.005078\n",
            "Control_adj   165  15753   114    51  15738    15  0.690909     0.883721  0.775510           6.502073             14.229175  0.004190\n",
            "Experimental  165  15753   136    29  15578   175  0.824242     0.437299  0.571429           4.743058             15.988189  0.012950\n",
            "9:3:2019-10-31 21:58:15.016812\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       165  15753    88    77  15737    16  0.533333     0.846154  0.654275           9.775097             10.956150  0.005904\n",
            "Control_adj   165  15753   108    57  15729    24  0.654545     0.818182  0.727273           7.312476             13.418771  0.005142\n",
            "Experimental  165  15753   154    11  15412   341  0.933333     0.311111  0.466667           3.524312             17.206936  0.022345\n",
            "9:4:2019-10-31 22:00:52.096786\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       165  15753    84    81  15744     9  0.509091     0.903226  0.651163          10.233698             10.497550  0.005713\n",
            "Control_adj   165  15753   113    52  15723    30  0.684848     0.790210  0.733766           6.721950             14.009298  0.005205\n",
            "Experimental  165  15753   146    19  15603   150  0.884848     0.493243  0.633406           3.329564             17.401684  0.010728\n",
            "9:5:2019-10-31 22:03:29.269368\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       165  15753    90    75  15743    10  0.545455     0.900000  0.679245           9.486116             11.245131  0.005396\n",
            "Control_adj   165  15753   111    54  15733    20  0.672727     0.847328  0.750000           6.910416             13.820832  0.004698\n",
            "Experimental  165  15753   144    21  15615   138  0.872727     0.510638  0.644295           3.505466             17.225782  0.010093\n",
            "9:6:2019-10-31 22:06:06.569327\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       165  15753    90    75  15738    15  0.545455     0.857143  0.666667           9.517527             11.213720  0.005713\n",
            "Control_adj   165  15753   119    46  15712    41  0.721212     0.743750  0.732308           6.037191             14.694057  0.005523\n",
            "Experimental  165  15753   144    21  15409   344  0.872727     0.295082  0.441041           4.799598             15.931650  0.023170\n",
            "9:7:2019-10-31 22:08:44.820840\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       165  15753    79    86  15737    16  0.478788     0.831579  0.607692          10.905893              9.825355  0.006475\n",
            "Control_adj   165  15753   118    47  15678    75  0.715152     0.611399  0.659218           6.376429             14.354818  0.007745\n",
            "Experimental  165  15753   129    36  15592   161  0.781818     0.444828  0.567033           5.534615             15.196633  0.012506\n",
            "9:8:2019-10-31 22:11:26.321175\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision          F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  ----------  -----------------  --------------------  --------\n",
            "Control       165  15753     0   165  15753     0  0.000000   nan         nan                 20.731248              0.000000  0.010474\n",
            "Control_adj   165  15753   125    40  15697    56  0.757576     0.690608    0.722543           5.377560             15.353688  0.006094\n",
            "Experimental  165  15753   147    18  15566   187  0.890909     0.440120    0.589178           3.436361             17.294886  0.013013\n",
            "9:9:2019-10-31 22:14:07.976501\n",
            "                P      N    TP    FN     TN    FP    Recall    Precision        F1    Real World Cost    Real World Benefit       Err\n",
            "------------  ---  -----  ----  ----  -----  ----  --------  -----------  --------  -----------------  --------------------  --------\n",
            "Control       165  15753    90    75  15736    17  0.545455     0.841121  0.661765           9.530092             11.201156  0.005840\n",
            "Control_adj   165  15753   120    45  15709    44  0.727273     0.731707  0.729483           5.930393             14.800854  0.005650\n",
            "Experimental  165  15753   136    29  15600   153  0.824242     0.470588  0.599119           4.604850             16.126398  0.011553\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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uZiu9ZKwCo6lx1sansHyLRqWLWi1NrthN2Yni6AofGFgss34yz2IyydH+XmY6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\nCcqgKxQKxUXC/wETVEBT3+epHgAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "f-9wH-4bHFr_",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 292
        },
        "outputId": "ffccfa36-62f4-439d-e0e9-16a4fadd6331"
      },
      "source": [
        "control1_test_p_values = np.zeros((12,1))\n",
        "control2_test_p_values = np.zeros((12,1))\n",
        "\n",
        "for i in range(stats.shape[2]):\n",
        "  _, control1_test_p_values[i] = sp.stats.ttest_rel(stats[:, 0, i], stats[:, 2, i])\n",
        "  _, control2_test_p_values[i] = sp.stats.ttest_rel(stats[:, 1, i], stats[:, 2, i])\n",
        "\n",
        "print (\"n=\" + str(stats.shape[0]))\n",
        "  \n",
        "print(tabulate([('Control',) + tuple(np.mean(stats[:,0,:], axis=0)), \\\n",
        "                ('Control_adj',) + tuple(np.mean(stats[:,1,:], axis=0)), \\\n",
        "                ('Experimental',) + tuple(np.mean(stats[:,2,:], axis=0)), \\\n",
        "                ('control1_p_values',) + tuple(control1_test_p_values), \\\n",
        "                ('control2_p_values',) + tuple(control2_test_p_values) \\\n",
        "               ], \\\n",
        "               headers=['P', 'N', 'TP', \"FN\", \"TN\", \"FP\", \"Recall\", \\\n",
        "                        \"Precision\", \"F1\", \"Real World Cost\", \\\n",
        "                        \"Real World Benefit\", \"Err\"], \\\n",
        "               floatfmt=\".20f\"))\n",
        "\n",
        "print(tabulate([('Control',) + tuple(np.mean(stats[:,0,:], axis=0)), \\\n",
        "                ('Control_adj',) + tuple(np.mean(stats[:,1,:], axis=0)), \\\n",
        "                ('Experimental',) + tuple(np.mean(stats[:,2,:], axis=0)), \\\n",
        "                ('control1_p_values',) + tuple(control1_test_p_values), \\\n",
        "                ('control2_p_values',) + tuple(control2_test_p_values) \\\n",
        "               ], \\\n",
        "               headers=['P', 'N', 'TP', \"FN\", \"TN\", \"FP\", \"Recall\", \\\n",
        "                        \"Precision\", \"F1\", \"Real World Cost\", \\\n",
        "                        \"Real World Benefit\", \"Err\"], \\\n",
        "               floatfmt=\".20e\"))\n"
      ],
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "n=100\n",
            "                                          P                           N                        TP                       FN                          TN                        FP                  Recall                 Precision                        F1         Real World Cost       Real World Benefit                     Err\n",
            "-----------------  ------------------------  --------------------------  ------------------------  -----------------------  --------------------------  ------------------------  ----------------------  ------------------------  ------------------------  ----------------------  -----------------------  ----------------------\n",
            "Control            164.69999999999998863132  15743.29999999999927240424  119.28000000000000113687  45.42000000000000170530  15730.64999999999963620212   12.65000000000000035527  0.72462614620498710938  nan                       nan                       5.78193359429067843536  14.92494230878920014050  0.00368466369279095169\n",
            "Control_adj        164.69999999999998863132  15743.29999999999927240424  132.99000000000000909495  31.71000000000000085265  15722.95999999999912688509   20.33999999999999985789  0.80757219528341495085    0.86938146286681006192    0.83597294273512645635  4.11033981948990412292  16.59653608358997090022  0.00330264187470912483\n",
            "Experimental       164.69999999999998863132  15743.29999999999927240424  148.62999999999999545253  16.07000000000000028422  15616.13999999999941792339  127.15999999999999658939  0.90244528495134135326    0.56968442803501606608    0.69073569272813695186  2.81662658343590965870  17.89024931964397779893  0.00908987404317638213\n",
            "control1_p_values  nan                         nan                         0.00000000000000000000   0.00000000000000000000      0.00000000000000000000    0.00000000000000000000  0.00000000000000000000  nan                       nan                       0.00000000000000000231   0.00000000000000000231  0.00000000000000000000\n",
            "control2_p_values  nan                         nan                         0.00000000000000000000   0.00000000000000000000      0.00000000000000000000    0.00000000000000000000  0.00000000000000000000    0.00000000000000000000    0.00000000000000000000  0.00000000000000000000   0.00000000000000000000  0.00000000000000000000\n",
            "                                              P                             N                          TP                          FN                          TN                          FP                      Recall                     Precision                            F1             Real World Cost          Real World Benefit                         Err\n",
            "-----------------  ----------------------------  ----------------------------  --------------------------  --------------------------  --------------------------  --------------------------  --------------------------  ----------------------------  ----------------------------  --------------------------  --------------------------  --------------------------\n",
            "Control              1.64699999999999988631e+02    1.57432999999999992724e+04  1.19280000000000001137e+02  4.54200000000000017053e+01  1.57306499999999996362e+04  1.26500000000000003553e+01  7.24626146204987109378e-01  nan                           nan                           5.78193359429067843536e+00  1.49249423087892001405e+01  3.68466369279095169037e-03\n",
            "Control_adj          1.64699999999999988631e+02    1.57432999999999992724e+04  1.32990000000000009095e+02  3.17100000000000008527e+01  1.57229599999999991269e+04  2.03399999999999998579e+01  8.07572195283414950850e-01    8.69381462866810061918e-01    8.35972942735126456348e-01  4.11033981948990412292e+00  1.65965360835899709002e+01  3.30264187470912483346e-03\n",
            "Experimental         1.64699999999999988631e+02    1.57432999999999992724e+04  1.48629999999999995453e+02  1.60700000000000002842e+01  1.56161399999999994179e+04  1.27159999999999996589e+02  9.02445284951341353263e-01    5.69684428035016066083e-01    6.90735692728136951857e-01  2.81662658343590965870e+00  1.78902493196439777989e+01  9.08987404317638213180e-03\n",
            "control1_p_values  nan                           nan                           1.27548499657552001118e-21  1.27548499657552001118e-21  3.10604896875929358970e-28  3.10604896875929358970e-28  8.48625893383207608508e-22  nan                           nan                           2.30860410967123381273e-18  2.30860410967123381273e-18  3.02958818060357840003e-24\n",
            "control2_p_values  nan                           nan                           2.69823261110047099882e-35  2.69823261110047099882e-35  2.54086383042267603295e-28  2.54086383042267603295e-28  1.85547078735290434622e-35    8.65709918512337789545e-49    6.47886652663407226973e-35  3.10398363839630837661e-27  3.10398363839621941097e-27  1.79362907093110064185e-25\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yHEB51REPE6U",
        "colab_type": "text"
      },
      "source": [
        "\n",
        "# Graphical Display of Loss Function Mechanics"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9VASnHSpPPlc",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 531
        },
        "outputId": "353ecd79-5048-42e1-f2c4-3dbffa5becd1"
      },
      "source": [
        "def J(z, y):\n",
        "  if (y==1):\n",
        "    return -np.log(z)\n",
        "  elif (y==0):\n",
        "    return -np.log(1-z)\n",
        "  else:\n",
        "    assert false\n",
        "\n",
        "def J_batch(p, n_h, n_t):\n",
        "  m = n_h + n_t\n",
        "  x = np.zeros(m)\n",
        "\n",
        "  for i in range(0,n_h):\n",
        "    x[i] = 1\n",
        "\n",
        "  retval = 0.\n",
        "  for i in range(0, m):\n",
        "    retval += J(p, x[i])\n",
        "  retval /= x.shape[0]\n",
        "  return retval\n",
        "\n",
        "x_and_y = []\n",
        "    \n",
        "for i in np.linspace(0.0001, 0.9999, 1000):\n",
        "  x_and_y.append((i, J_batch(i, 9, 1)))\n",
        "\n",
        "x_and_y = np.array(x_and_y)\n",
        "\n",
        "print(x_and_y.shape)\n",
        "  \n",
        "fig = plt.figure(figsize=(10,8))\n",
        "plt.plot(x_and_y[:,0], x_and_y[:,1])\n",
        "plt.xlabel('p')\n",
        "plt.ylabel('Loss')\n"
      ],
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(1000, 2)\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'Loss')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 18
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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AhSLbYcFvSXpQUnPm8dPMsWltRkWxJMIVAADInWzDVYNz7lvOuYnM49uSGjzWlReNVQfD\nFZPaAQBAbmQbrvab2a1mFs08bpW032dh+VBbmlAsYtpDzxUAAMiRbMPVHyi9DMMeSbsl3SzpI55q\nyptIxDSjoohhQQAAkDNZhSvn3Hbn3I3OuQbn3Azn3O+oAO4WlKSZVcWEKwAAkDPZ9lwdy2dyVkWA\nmqtKtKuHcAUAAHLjTMKV5ayKALXUlqije1iplAu6FAAAUADOJFwVRBppqSnVWDKlLvYYBAAAOXDC\nFdrNrF/HDlEmKaslzc0sKmm1pA7n3A2nXKFnLTXp38bOA0OaWVkccDUAAGC6O2G4cs5V5KCNP5P0\nmqTKHHxXzs2uKZUktXcPq6012FoAAMD0dybDgieV2SLn3ZK+4bOdM3Gw56q9eyjgSgAAQCHwGq4k\n/W9Jfykp5bmd01Ycj6q+vEjt3cNBlwIAAAqAt3BlZjdI6nTOrTnJeavMbLWZre7q6vJVzgm11JRo\nJz1XAAAgB3z2XF0u6UYz2ybph5KuMbPvHX2Sc+5O51ybc66toSGY7Qpb60q1bR/hCgAAnDlv4co5\n93nnXItzrlXShyQ96py71Vd7Z2JBQ7k6eoY1PJYMuhQAADDN+Z5zNS3MbyiXJG3ZNxBwJQAAYLrL\nS7hyzj0+Fde4OmjBjDJJ0pauwYArAQAA0x09V5Ja68pkJm3uoucKAACcGcKV0ssxzKouoecKAACc\nMcJVxoKGcnquAADAGSNcZcxvKNOWrkGlUgWxHzUAAAgI4SpjQUO5hseT2tM3EnQpAABgGiNcZcxv\nSN8xyNAgAAA4E4SrjLNmVkiSNu7uD7gSAAAwnRGuMurKi9RYWawNu/uCLgUAAExjhKvDLGuu1IZd\nhCsAAHD6CFeHWdpcqU1dAxoZZ49BAABweghXh1naVKlkyumNvcy7AgAAp4dwdZilzZWSxNAgAAA4\nbYSrw8yuKVVFUYxJ7QAA4LQRrg4TiZjObqrUq/RcAQCA00S4Oso5LVVa39GrsYlU0KUAAIBpiHB1\nlAvm1Gh0IqXXGBoEAACngXB1lAvmVkuS1u7oDrgSAAAwHRGujtJUVaKmqmKt3dETdCkAAGAaIlwd\nwwVzarR2Oz1XAADg1BGujmHFnGp19Ayrs28k6FIAAMA0Q7g6hgvm1kiSVtN7BQAAThHh6hiWN1ep\nJB7Vs1v2B10KAACYZghXx5CIRXTRvFo9s5lwBQAATg3h6jguW1CnNzsH1NnPvCsAAJA9wtVxXLag\nTpLovQIAAKeEcHUcy5qrVFEcI1wBAIBTQrg6jmjEtHJ+nX6zaZ+cc0GXAwAApgnC1QlcfVaD2ruH\ntblrIOhSAADANEG4OoFrlsyQJD3yWmfAlQAAgOmCcHUCTVUlWtpUqUc2Eq4AAEB2CFcnce3ZM7Rm\ne7d6hsaCLgUAAEwDhKuTuGbJDCVTTr9+oyvoUgAAwDRAuDqJ81qqVVeW0KMMDQIAgCwQrk4iEjG9\nbckMPbaxU2MTqaDLAQAAUxzhKgvvPqdJfSMTevJNhgYBAMCJEa6ycPnCelWXxvXTl3cFXQoAAJji\nCFdZSMQiun5Zo365Ya9GxpNBlwMAAKYwwlWW3nNeswbHknqMie0AAOAECFdZWjm/TvXlRfrpOoYG\nAQDA8RGushSNmN59TqMeea1TvcPjQZcDAACmKMLVKfhA22yNTqT04EsdQZcCAACmKG/hysyKzex5\nM3vZzF41s7/11Va+LJ9VpWXNlfrhCzuDLgUAAExRPnuuRiVd45w7T9L5kq43s5Ue28uL/3LRbL26\nq0/rO3qDLgUAAExB3sKVSxvIvI1nHs5Xe/ly03mzlIhF9CN6rwAAwDF4nXNlZlEze0lSp6RfOuee\nO8Y5q8xstZmt7uqa+iugV5XG9a7ljfrJix0aHJ0IuhwAADDFeA1Xzrmkc+58SS2SLjaz5cc4507n\nXJtzrq2hocFnOTnz4Uvnqn90QvevbQ+6FAAAMMXk5W5B51yPpMckXZ+P9ny7YE6Nzm2p0ree3qZU\natqPdAIAgBzyebdgg5lVZ16XSLpO0kZf7eWTmemjl7dqS9egnmAzZwAAcBifPVdNkh4zs3WSXlB6\nztXPPLaXV+8+p1kNFUX61lPbgi4FAABMITFfX+ycWydpha/vD1oiFtFtK+fqS798Q6/t7tPZTZVB\nlwQAAKYAVmg/A7dd2qryopj+z6Obgi4FAABMEYSrM1BVGtdtl87Vz9fv1qbO/qDLAQAAUwDh6gx9\n7Ip5Ko5F9ZXHNgddCgAAmAIIV2eorrxIv3fJHP37Sx3avn8w6HIAAEDACFc5sOqq+YpFI/rnR94M\nuhQAABAwwlUOzKgs1kcua9UDL3Zow66+oMsBAAABIlzlyJ9cvUAVRTF98aGCWCcVAACcJsJVjlSX\nJvSnb1uoX7/Rpac37Qu6HAAAEBDCVQ79/mWtmlVdov/vPzey5yAAACFFuMqh4nhUf/Hbi/VKR6/u\nXdMedDkAACAAhKsc+53zZ6ltbo3+/4c2qmdoLOhyAABAnhGuciwSMX3hpuXqGRrTl37xRtDlAACA\nPCNcebC0uVK3Xdqq7z23Xa+09wZdDgAAyCPClSef+e3Fqisr0ucfWKfxZCrocgAAQJ4QrjypLI7r\n//2dZVrf0aev/5p9BwEACAvClUfXL2/SDec26Z8feVOv7+kPuhwAAJAHhCvP/vbGZaosjuuz97ys\nCYYHAQAoeIQrz+rKi/SFm5brlY5e3cHwIAAABY9wlQfvPjc9PPhPv3pTa7Z3B10OAADwiHCVJ3//\n3nPUVFWsT939onqHx4MuBwAAeEK4ypOqkrhuv2WF9vaN6HP3rZNz7D0IAEAhIlzl0QVzavTZd5yl\n/1y/R99/bkfQ5QAAAA8IV3m26sr5umpxg77w0w1au4P5VwAAFBrCVZ5FIqbbP3S+GquK9fG71qiz\nbyTokgAAQA4RrgJQXZrQnbddqP6RCX38e2s0OpEMuiQAAJAjhKuALGms1Jc+eJ7W7ujR//jJeia4\nAwBQIAhXAXrXOU365DUL9ePV7frKY5uCLgcAAORALOgCwu4z1y1We/ew/vEXb2hWTYneu6Il6JIA\nAMAZIFwFzMz0xfefqz29I/rLe9dpZkWxLltYH3RZAADgNDEsOAUkYhHd8eELNa++TH901xpt2NUX\ndEkAAOA0Ea6miKqSuL790YtVXhzTh//tOW3q7A+6JAAAcBoIV1NIc3WJvv+Hl8jM9Lv/+py27RsM\nuiQAAHCKCFdTzPyGcn3/Dy/ReDKl3/vGc+roGQ66JAAAcAoIV1PQWY0Vuutjl6hvZFy33Pms2ruH\ngi4JAABkiXA1RS2fVaW7PnaJeobG9ME7ntFWhggBAJgWCFdT2Pmzq3X3qpUamUjpA3c8o9f3MMkd\nAICpjnA1xS1rrtKP/2ilIiZ96M5n9Ep7b9AlAQCAEyBcTQMLZ1Tono9fqtJETLf867N68s2uoEsC\nAADHQbiaJubWleneP75ULTUl+ui3XtC9a9qDLgkAABwD4Woaaaoq0Y8/fqkumV+rz97zsm5/5E05\n54IuCwAAHMZbuDKz2Wb2mJltMLNXzezPfLUVJpXFcX3rIxfrfRfM0pd/+Yb++33rNDaRCrosAACQ\n4XPj5glJf+GcW2tmFZLWmNkvnXMbPLYZColYRF/6wHlqqSnV7Y+8qS1dg/rqrRdoRkVx0KUBABB6\n3nqunHO7nXNrM6/7Jb0maZav9sLGzPSZ6xbr//zuCr26q083/stTenlnT9BlAQAQenmZc2VmrZJW\nSHouH+2FyQ3nNuu+P75MsajpA19/honuAAAEzHu4MrNySfdJ+rRzru8Yn68ys9VmtrqriyUGTsfS\n5ko9+Ikr1Da3Rp+952X99b+v18h4MuiyAAAIJa/hysziSger7zvn7j/WOc65O51zbc65toaGBp/l\nFLTasoS++wcX6w+vmKfvPrNd7//a09rGljkAAOSdz7sFTdK/SXrNOfdlX+3gkFg0or+6Yam+cVub\n2ruHdcO//EYPvrwr6LIAAAgVnz1Xl0v6sKRrzOylzONdHttDxtuXztTP/+xKndVYoU/d/aI+f/86\nDY1NBF0WAACh4G0pBufcbySZr+/Hic2qLtEPV63Ul3/5hu749WY9s3m/vvTB83Xh3JqgSwMAoKCx\nQnsBi0cj+u/XL9Hd/3WlxpNOH7jjaf2vhzey6CgAAB4RrkJg5fw6PfTpK/WBC2frK49t1k1feUob\n97zlxk0AAJADhKuQqCiO64s3n6tv3Namrv4R3fgvT+mff/UmvVgAAOQY4Spk3r50ph7+9FW6fnmj\n/ulXb+jdtz+p1dsOBF0WAAAFg3AVQnXlRbr9lhX61kcu0tBYUjff8Yz+6ievqG9kPOjSAACY9ghX\nIfa2JTP0iz+/Sn9w+Tz94Lkduu7Lv9aDL++Scy7o0gAAmLYIVyFXVhTTX79nqR74k8tVX16kT939\nov7Lnc/qtd1MeAcA4HQQriBJOm92tR78xBX6+/cu15t7+/Xu25/UX//7evUMjQVdGgAA0wrhCpOi\nEdPvXTJXj332at26cq6+9+x2ve0fH9f3nt2uiSR3FQIAkA3CFd6iujShL9y0XD/75JVaNLNCf/WT\n9XrH/35Cv3h1D/OxAAA4CcIVjmtpc6V+tGqlvv7hC+UkrbprjT749We0dkd30KUBADBlEa5wQmam\ndyxr1C8+fZX+/r3LtXXfkN731af1x99boy1dA0GXBwDAlGNTaZinra3NrV69OugycAKDoxP6xpNb\n9fUnNmt0IqX3rpilT12zSHPqSoMuDQCAvDKzNc65trccJ1zhdHT1j+prj2/W95/bromU0/svmKVP\nXrNIs2sJWQCAcCBcwYvOvhF99fHN+sHzO5RKOd18YYv+9G0LCVkAgIJHuIJXe3pH9LXHN+nu53fK\nyel9K1q06rfma0FDedClAQDgBeEKebG7d1hfe3yzfvTCTo0lU3rH0kZ9/OoFOn92ddClAQCQU4Qr\n5NW+gVF95+lt+s7T29Q3MqGV82v1x1cv1FWL6mVmQZcHAMAZI1whEAOjE/rh8zv0jSe3ak/fiJY2\nVWrVVfP1rnOalIixEggAYPoiXCFQYxMp/eSlDn3915u1uWtQDRVFuvWSufrdS+aooaIo6PIAADhl\nhCtMCamU0xNvdunbT2/T4693KRGN6D3nNeujl7dq+ayqoMsDACBrxwtXsSCKQXhFIqarz5qhq8+a\noc1dA/rO09t075p23be2XRe11ui2S1v1jmWNDBkCAKYteq4QuL6Rcf34hZ36zjPbtPPAsOrKErq5\nrUW3XDRHrfVlQZcHAMAxMSyIKS+ZcnryzS794LkdemRjp5IppysW1uuWi+fouqUz6c0CAEwphCtM\nK3t6R/Tj1Tv1oxd2qqNnWPXlRfpAW4s+2DZb8+jNAgBMAYQrTEvJlNMTb3Tp+8/t0KMb9yrlpAvn\n1ujmC1v07nObVFkcD7pEAEBIEa4w7e3tG9EDL3bo3jXt2tQ5oKJYRO9Y1qibL2zR5QvrFY2wOCkA\nIH8IVygYzjmta+/VvWva9eDLu9Q7PK7GymK994JZeu+KWVo8syLoEgEAIUC4QkEanUjqkdc6dd+a\ndj3+RpeSKacljRV6z3nNes+5zZpTVxp0iQCAAkW4QsHr6h/Vz1/ZrQdf3qU127slSefPrtZ7zmvW\nDec2aWZlccAVAgAKCeEKodLePaSfrdutB1/apQ27+2QmXTKvVu85r1nvXN6k2rJE0CUCAKY5whVC\na1PngH768i799OVd2rJvUBGTLplXp+uXN+odyxrVWEWPFgDg1BGuEHrOOb26q08Prd+j/1y/W5u7\nBiVJK+ZU6/pl6aDFivAAgGwRroCjbOrs10Pr9+ihV/dofUefJGlJY4WuX96o65c36qyZFTJjeQcA\nwLERroAT2HlgSA+/ukcPv7pHq7d3yzmppaZE1y6ZoWvOnqmV82tVFIsGXSYAYAohXAFZ6uwf0a82\ndOrRjXv1m037NDKeUmkiqisX1evaJTN19ZIGzahgnhYAhB3hCjgNI+NJPbN5vx7ZuFePvtapXb0j\nkqTzWqp0zZKZuvbsGVrWXMnwIQCEEOEKOEPOOW3c069HN3bqkdf26sWdPXJOqi8v0lWL6nXl4npd\nsbBBDRVFQZcKAMgDwhWQY/sGRvX461164o0u/WbTPh0YHJMkLW2q1FWLG3TV4npdOLeGuVoAUKAI\nV4BHqVR6mYcn3kyHrTXbu2pKt3UAABL1SURBVDWRcipNRLVyfp2uXFSvqxY3aH59GUOIAFAgCFdA\nHg2MTuiZzfv1ZCZsbds/JEmaWVmkyxbU69L5dbp0QZ1m17L3IQBMV8cLVzGPDX5T0g2SOp1zy321\nA0xF5UUxXbd0pq5bOlOStGP/kJ7c1DUZuB54sUNSermHS+fX6bKFdbp0fj2rxQNAAfDWc2VmV0ka\nkPTdbMMVPVcIA+ec3uwc0DOb9+vpzfv07JYD6h0elyTNry/TygV1umxBnVbOr1N9OZPjAWCqCmRY\n0MxaJf2McAUcXyrltGF3n57dsl9Pb96v57ce0MDohKR02GprrdFFrbW6eF6t5tSWMmcLAKaIvA8L\nAshOJGJaPqtKy2dV6Q+vnK+JZEqvdPTq+a0H9MK2A3r41b368ep2SdKMiiJd1Fqri1prdNG8Wi1p\nrFQ0QtgCgKkk8J4rM1slaZUkzZkz58Lt27d7qweYjlIpp01dA5Nha/W2bnX0DEuSKopiumBujS6e\nV6u2uTU6t6VaJQmWfgCAfGBYECggHT3DeiETtl7YdkBv7B2QJEUjprObKrRido1WzKnWijk1aq1j\nKBEAfGBYECggs6pLNGvFLP3OilmSpO7BMa3d0a2XdvZo7Y5uPfBih+56Nt0LXFMa14o5NVoxOx22\nzp1dpcrieJDlA4A3r+/pV0fPkK5ZMjOwGnwuxXC3pKsl1ZtZu6S/cc79m6/2gDCrKUvo2rNn6tqz\n0z9MkimnTZ0DenFHt9bu6NaLO3r06MZOSZKZtGhG+WTv1rkt1Vo0s1zxaCTI3wIA5MS9a3bqrme3\na+PfvTOwGryFK+fcLb6+G8CJRSOmsxordFZjhT508RxJUu/wuNa192jt9h69uLNbD726Rz9avVOS\nVBSLaGlzpc6dVaVzWqp1bkuVFjSUM1kewLQzNJZUaSLYgTmGBYGQqCqJ68pFDbpyUYOk9HpbW/cN\n6pWOXr3S3qt1Hb26Z027vvNMejixNBHVsuZKnTMrHbbOaanSvLoyRQhcAKaw4bGkSuLB3thDuAJC\nysw0v6Fc8xvKddP56blbyZTT1n0DWtfeq3XtvXqlo1c/eH67vvlUSlJ65fnlsyp1bku1ljVXallz\npebV08MFYOpI91wRrgBMEdGIaeGMCi2cUaH3XdAiSZpIprSpKx24DvZwffupbRpLpgNXcTyisxor\ntbSpUkub089LGitUVsSPFwD5NzROuAIwxcWiES1prNSSxkp9sG22JGk8mdKmzgFt2NWnDbv7tGFX\nn37+ym7d/fwOSelJ8/PqynR286HQtaypUg0VRSwLAcCr4bGJwNf7I1wBOGXxaERnN1Xq7KZKvT9z\nzDmnXb0j6cC1q08bdvdqXXuP/mPd7slfV1+e0NlNlTprZsXkhPtFMyoC/0EIoHAMjyc1o6I40BoI\nVwBywszS629Vl+i6pYfWl+kdHtfG3Yd6uDbs7tNdz27X6EQq8+ukubWlWjyzQksaK7S4Mf3cWlem\nGMtDADhFQ2PJwP/BRrgC4FVVSVyXzK/TJfPrJo8lU07b9w/q9T39en1vv97Y26+Ne/r1q9f2KpXZ\nNCIRjWh+Q9lk4DrY2zWruoShRQDHNTyWVCl3CwIIm2jk0J2K7zynafL4yHhSm7sGJkPX63v69fzW\nA/rJS7smzylLRLVgRrkWNpSnnzOPObWlLIQKgLsFAeBwxfGoljVXaVlz1RHH+0bG9UYmcL25d0Cb\nOgf09Ob9uv/Fjslz4lHT3LoyLWw4FLgWzijX/IaywBcUBJA/w2NJlbCIKACcWGVxXG2ttWprrT3i\neP/IuDZ3DWpT54A2d6VD1xt7+/XL1/YqmTq0Kf2s6pLJsLWgoVwLGso0r6FMDeXcvQgUkolkSmPJ\nFD1XAHC6KorjOn92tc6fXX3E8dGJpLbvH9KmzoEjHs9t3a+R8dTkeWWJqOY1lKm1rkzz68sOe12u\nqlI2twammwNDY5KkymJ6rgAgp4piUS2eWaHFMyuOOJ5KOXX0DGvLvkFt2zeorfsGtWXfoNa19+rn\nr+zWYZ1dqimNa159mebVl2tefanm1Zertb5U8+oZZgSmqs2dg5Kk+Q3lgdbBTwgAoRGJmGbXlmp2\nbal+a3HDEZ+NTiS188CwtmaC15Z9g9q6b0BPbdqn+9aOHHFuY2WxWutLNbe2THPqSjWntlRzM8/V\npYl8/pYAHGZT14AkaeEMwhUABK4oFp2cl3W0obEJbds3lA5e+we1pSsdvB7Z2Kl9A6NHnFtZHNOc\nunTwml17ZPBqqipm7S7Aow27+lRRFFNTFYuIAsCUVpqIpfdNbK58y2eDoxPa2T2k7fuHtPPAkHYc\nSL9+bXeffrFhj8aTh8YaYxHTrJoSzcmEroPBq6WmVC01JaoqiTPBHjgDT23ap4vn1Qb+54hwBQBn\noKwoNrn34tGSKac9fSPavn9QOzOha8eBdAj7j1d2q2do/Ijzy4ti6VXua0rUUpNe7b6lplSzMq/r\nyxOB/6UBTFWv7+nXjgND+tgV84IuhXAFAL5EI4e2BNKCt37eOzyunQeG1N49pPbu4clHR8+wXth2\nQP0jE0ecXxyPqPlg4KpOB7DDQ9iMiiJFIoQvhNPdz+9QLGK64dymk5/sGeEKAAJSVRJX1awqLZ9V\ndczP+0bG1XEwcGUCWEdP+v36jl4dGBw74vx41NRUVaKmquL0o/rg60PHasvo/ULhae8e0g9f2KEb\nz29WXXlR0OUQrgBgqqosjquyKa6zm9465CilJ9p3dA+rvedgAEuHrz29w3phW7f29u3WxOHrS0hK\nxCJqqipWY2WxmqtL1FhVrOaqYjUSwDBNpVJOn7//FUXM9JnrFgddjiTCFQBMW6WJmBbNrNCio9bz\nOiiVcto3MKrdvSOZx7D29I5oV++I9vQO6/mtB7S3b+S4AexgCJtZWayGiiLNrCzWjIPPlUWs94XA\nOef0Dw+/riff3Ke/u2mZWmpKgy5JEuEKAApWJGKaUVmsGZXFOm/2sc85MoANHxbERrS7Z1hrdnRr\nb9+oxiZSb/m1FUUxzag8MnQdDGEHjxHC4Mt4MqW//emr+t6zO/R7l8zRrSvnBl3SJP6PB4AQOzKA\nVR/zHOeceofH1dk/qr19I+rsG9Xe/vRzZ/+I9vaNZh3C6suL0o+KROZ1YvJYXXlCRbFg94TD9PD6\nnn597v51enFHj/7ot+brL9+xZEoNZROuAAAnZGaqLk2oujTxli2FDuecU9/whPb2jxw3hL3c3qN9\n/aMaHEse8zsqimNqOCxsHR7G6sqK1FBx6FhpIjql/kKFf5u7BvTVxzbrJy91qKokrttvWaEbz2sO\nuqy3IFwBAHLCzFRVGldVafyEIUyShseS2jcwmnmMpZ/7M+8Hx7Svf1Rv7O3X05v3q3d4/JjfURKP\nqrYsoZqyuGpKE6opTai2LKHq0nj6+DHeF8fpGZtueofH9dD63bp/bYee23pAxfGIbrt0rj55zSLV\nlk3N7aYIVwCAvCtJRCf3eTyZsYmUDgymA1jXwKj2HxbGDgyNqWdoXAcGx7TjwJC6B8fUd9T6YEe0\ne5xAVlOaDmGVJTFVlcRVWRxPP5ekn4tiEXrJ8qRvZFzrO3r17JYDevLNLr28s0cpJ82vL9NfXLdY\nt1wyR/VTYLmFEyFcAQCmtEQsosaqYjVmuV/ceDKlnqFx9QyN6cDgmLqHxnRgcFzdQ2PqHhw75UAm\nSYloRJUlh8LXkQHsyEBWXhxTWVFM5UWZ50RMZUVR9pU8Su/QuLbuT2+UvnXfoDZ3DWh9R6+27R+S\nJEVMOm92tT7xtoW65uyZOq+latoEXMIVAKCgxKMRNVQUqaEi+96N8WRKfcPj6huZUO/wuHqHx9V3\n8Hnk0Pu+4fTnBwbHtHXf4OTxo1azOKaiWEQVmeBVljgYvqJHBrGimEoTURXHoyqORzLPmUcs/b4k\nEVVxLP15Uea8RDTYnrWxiZT6R8bVPzKReaT/W/Zn/tt19o+qs28k/Zx5fXigNZOaq0q0fFalbr6w\nRee0VOv8lmpVlcYD+z2dCcIVACD04tGI6sqLTmt1b+ecBkYn0sFsaFwDoxMaHJ046jmpwbH064GR\nQ8e7Bka1bf/Q5LlDx5nofzIRS/fwxSMRxaKmWDSieMQUjdqhY5PP6c9jma2SnJOc3ORrSel3k6+d\nxiZSGp1IaSyZ0thE5pF5PTqRUvIk6TIRi6SX5qgo0sKGcl22oE4tNSVqrStTa32Z5tSWFtR8OMIV\nAABnwMxUURxXRXE8vY/kGUimnEbGkxoZT2p4PKmR8ZRGxpManUi/Hh5LamTi0PFDj5RGJ5KaSDlN\nJJ0mUqnMs9N4MnXoWObz8UwwOtjZZTJp8nXmEckcl6m0NKZELKJELKKiaGTydSLzuiQeVUVxLPPf\n4dDzwXlrlcWxaTOklwuEKwAApohoxNLDhkX89TydMbsOAAAghwhXAAAAOUS4AgAAyCHCFQAAQA4R\nrgAAAHKIcAUAAJBDhCsAAIAcIlwBAADkEOEKAAAghwhXAAAAOeQ1XJnZ9Wb2upltMrPP+WwLAABg\nKvAWrswsKukrkt4paamkW8xsqa/2AAAApgKfPVcXS9rknNvinBuT9ENJN3lsDwAAIHA+w9UsSTsP\ne9+eOQYAAFCwAp/QbmarzGy1ma3u6uoKuhwAAIAz4jNcdUiafdj7lsyxIzjn7nTOtTnn2hoaGjyW\nAwAA4J/PcPWCpEVmNs/MEpI+JOlBj+0BAAAELubri51zE2b2CUkPS4pK+qZz7lVf7QEAAEwF5pwL\nuoZJZtYlabvnZuol7fPcBk4N12Rq4rpMPVyTqYnrMvXk65rMdc69ZU7TlApX+WBmq51zbUHXgUO4\nJlMT12Xq4ZpMTVyXqSfoaxL43YIAAACFhHAFAACQQ2EMV3cGXQDegmsyNXFdph6uydTEdZl6Ar0m\noZtzBQAA4FMYe64AAAC8KdhwZWbXm9nrZrbJzD53jM+LzOxHmc+fM7PW/FcZLllck8+Y2QYzW2dm\nj5jZ3CDqDJuTXZfDznu/mTkz464oz7K5Jmb2wcyfl1fN7Af5rjGMsvgZNsfMHjOzFzM/x94VRJ1h\nYWbfNLNOM1t/nM/NzG7PXK91ZnZBvmoryHBlZlFJX5H0TklLJd1iZkuPOu1jkrqdcwsl/ZOkL+a3\nynDJ8pq8KKnNOXeupHsl/UN+qwyfLK+LzKxC0p9Jei6/FYZPNtfEzBZJ+ryky51zyyR9Ou+FhkyW\nf1b+StKPnXMrlN6V5Kv5rTJ0vi3p+hN8/k5JizKPVZK+loeaJBVouJJ0saRNzrktzrkxST+UdNNR\n59wk6TuZ1/dKutbMLI81hs1Jr4lz7jHn3FDm7bNK70cJv7L5syJJf6f0P0BG8llcSGVzTf6rpK84\n57olyTnXmecawyib6+IkVWZeV0nalcf6Qsc594SkAyc45SZJ33Vpz0qqNrOmfNRWqOFqlqSdh71v\nzxw75jnOuQlJvZLq8lJdOGVzTQ73MUn/6bUiSFlcl0xX+mzn3H/ks7AQy+bPymJJi83sKTN71sxO\n9K935EY21+V/SrrVzNol/VzSJ/NTGo7jVP/eyRlvewsCp8vMbpXUJum3gq4l7MwsIunLkj4ScCk4\nUkzpoY6rle7hfcLMznHO9QRaFW6R9G3n3JfM7FJJd5nZcudcKujCkF+F2nPVIWn2Ye9bMseOeY6Z\nxZTuwt2fl+rCKZtrIjN7u6T/R9KNzrnRPNUWZie7LhWSlkt63My2SVop6UEmtXuVzZ+VdkkPOufG\nnXNbJb2hdNiCP9lcl49J+rEkOeeekVSs9B53CEZWf+/4UKjh6gVJi8xsnpkllJ5Y+OBR5zwo6fcz\nr2+W9Khj0S+fTnpNzGyFpK8rHayYQ5IfJ7wuzrle51y9c67VOdeq9Fy4G51zq4MpNxSy+fn1E6V7\nrWRm9UoPE27JZ5EhlM112SHpWkkys7OVDlddea0Sh3tQ0m2ZuwZXSup1zu3OR8MFOSzonJsws09I\nelhSVNI3nXOvmtkXJK12zj0o6d+U7rLdpPSEuA8FV3Hhy/Ka/C9J5ZLuydxbsMM5d2NgRYdAltcF\neZTlNXlY0m+b2QZJSUn/zTlHz7tHWV6Xv5D0r2b250pPbv8I/2j3x8zuVvofGfWZeW5/IykuSc65\nO5Se9/YuSZskDUn6aN5q47oDAADkTqEOCwIAAASCcAUAAJBDhCsAAIAcIlwBAADkEOEKAAAghwhX\nAAAAOUS4AgAAyCHCFYCCZGatZrbRzL5vZq+Z2b1mVhp0XQAKH+EKQCE7S9JXnXNnS+qT9CcB1wMg\nBAhXAArZTufcU5nX35N0RZDFAAgHwhWAQnb0/l7s9wXAO8IVgEI2x8wuzbz+XUm/CbIYAOFAuAJQ\nyF6X9Kdm9pqkGklfC7geACEQC7oAAPBowjl3a9BFAAgXeq4AAAByyJxjficAAECu0HMFAACQQ4Qr\nAACAHCJcAQAA5BDhCgAAIIcIVwAAADlEuAIAAMih/wu7SxZC9S0MNQAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 720x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "w2EfTMy9YS1q",
        "colab_type": "text"
      },
      "source": [
        "# Bernoulli Trial"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iWrXZk6VdYlW",
        "colab_type": "text"
      },
      "source": [
        "A quick Bernoulli trial. Bias should be close to 2.1. Sigmoid(2.1) = 0.9, which is the minimum cost / accurate prediction for 9 heads and 1 tail. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "v8faj_W8YcZm",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 85
        },
        "outputId": "92896d8b-13d5-463c-ec80-dfba887a04b6"
      },
      "source": [
        "k_y = k_x = Input(shape=(1,))\n",
        "k_y = Dense(1, activation='sigmoid', kernel_initializer='zeros',\n",
        "                bias_initializer='ones')(k_y)\n",
        "\n",
        "model_bernoulli = Model(inputs=k_x, outputs=k_y)\n",
        "model_bernoulli.compile(optimizer='adam', loss='binary_crossentropy', metrics=['binary_accuracy'])\n",
        "\n",
        "X = np.zeros((10,))\n",
        "y = np.concatenate([np.ones((9,)), np.zeros((1,))])\n",
        "\n",
        "model_bernoulli.fit(x = X, y = y, epochs=1000, verbose=0) \n",
        "print(model_bernoulli.evaluate(x = X, y = y))\n",
        "print(model_bernoulli.get_weights()[1])\n",
        "\n",
        "def sigmoid(x): return 1 / (1 + np.exp(-x))\n",
        "\n",
        "print(sigmoid(model_bernoulli.get_weights()[1][0]))\n"
      ],
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "\r10/10 [==============================] - 11s 1s/step\n",
            "[0.33524543046951294, 0.8999999761581421]\n",
            "[1.75]\n",
            "0.8518968557974441\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ay07zsdvMw1i",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}