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<ol class="chapter"><li class="chapter-item expanded affix "><a href="index.html">引言</a></li><li class="chapter-item expanded "><a href="chapter1.html"><strong aria-hidden="true">1.</strong> 机器学习策略的原因</a></li><li class="chapter-item expanded "><a href="chapter2.html"><strong aria-hidden="true">2.</strong> 如何使用本书来帮助您的团队</a></li><li class="chapter-item expanded "><a href="chapter3.html"><strong aria-hidden="true">3.</strong> 预备知识和注释</a></li><li class="chapter-item expanded "><a href="chapter4.html"><strong aria-hidden="true">4.</strong> 规模推动机器学习进步</a></li><li class="chapter-item expanded "><a href="chapter5.html"><strong aria-hidden="true">5.</strong> 您的开发和测试集</a></li><li class="chapter-item expanded "><a href="chapter6.html"><strong aria-hidden="true">6.</strong> 你的开发集和测试集应该来自相同的分布</a></li><li class="chapter-item expanded "><a href="chapter7.html"><strong aria-hidden="true">7.</strong> 开发集/测试集需要多大</a></li><li class="chapter-item expanded "><a href="chapter8.html"><strong aria-hidden="true">8.</strong> 为您的团队建立单一数字的评估指标以进行优化</a></li><li class="chapter-item expanded "><a href="chapter9.html"><strong aria-hidden="true">9.</strong> 优化指标和满足指标</a></li><li class="chapter-item expanded "><a href="chapter10.html"><strong aria-hidden="true">10.</strong> 通过开发集和评估标准加速迭代</a></li><li class="chapter-item expanded "><a href="chapter11.html"><strong aria-hidden="true">11.</strong> 何时更改开发/测试集和评估指标</a></li><li class="chapter-item expanded "><a href="chapter12.html"><strong aria-hidden="true">12.</strong> 小结：建立开发集和测试集</a></li><li class="chapter-item expanded "><a href="chapter13.html"><strong aria-hidden="true">13.</strong> 快速构建您的第一个系统，然后迭代</a></li><li class="chapter-item expanded "><a href="chapter14.html"><strong aria-hidden="true">14.</strong> 误差分析：查看开发集样本以评估想法</a></li><li class="chapter-item expanded "><a href="chapter15.html"><strong aria-hidden="true">15.</strong> 在误差分析期间并行评估多个想法</a></li><li class="chapter-item expanded "><a href="chapter16.html"><strong aria-hidden="true">16.</strong> 清理错误标注的开发和测试集样本</a></li><li class="chapter-item expanded "><a href="chapter17.html"><strong aria-hidden="true">17.</strong> 如果你有一个大的开发集，将其分成两个子集，只着眼于其中的一个</a></li><li class="chapter-item expanded "><a href="chapter18.html"><strong aria-hidden="true">18.</strong> Eyeball 和 Blackbox 开发集应该多大？</a></li><li class="chapter-item expanded "><a href="chapter19.html"><strong aria-hidden="true">19.</strong> 小贴士：基本误差分析</a></li><li class="chapter-item expanded "><a href="chapter20.html"><strong aria-hidden="true">20.</strong> 偏差和方差：误差的两大来源</a></li><li class="chapter-item expanded "><a href="chapter21.html"><strong aria-hidden="true">21.</strong> 偏差和方差的例子</a></li><li class="chapter-item expanded "><a href="chapter22.html"><strong aria-hidden="true">22.</strong> 比较最优错误率</a></li><li class="chapter-item expanded "><a href="chapter23.html"><strong aria-hidden="true">23.</strong> 处理偏差和方差</a></li><li class="chapter-item expanded "><a href="chapter24.html"><strong aria-hidden="true">24.</strong> 偏差和方差间的权衡</a></li><li class="chapter-item expanded "><a href="chapter25.html"><strong aria-hidden="true">25.</strong> 减少可避免偏差的方法</a></li><li class="chapter-item expanded "><a href="chapter26.html"><strong aria-hidden="true">26.</strong> 训练集上的误差分析</a></li><li class="chapter-item expanded "><a href="chapter27.html"><strong aria-hidden="true">27.</strong> 减少方差的方法</a></li><li class="chapter-item expanded "><a href="chapter28.html"><strong aria-hidden="true">28.</strong> 诊断偏差和方差：学习曲线</a></li><li class="chapter-item expanded "><a href="chapter29.html"><strong aria-hidden="true">29.</strong> 绘制训练误差曲线</a></li><li class="chapter-item expanded "><a href="chapter30.html"><strong aria-hidden="true">30.</strong> 解读学习曲线：高偏差</a></li><li class="chapter-item expanded "><a href="chapter31.html"><strong aria-hidden="true">31.</strong> 解释学习曲线：其他情况</a></li><li class="chapter-item expanded "><a href="chapter32.html" class="active"><strong aria-hidden="true">32.</strong> 绘制学习曲线</a></li><li class="chapter-item expanded "><a href="chapter33.html"><strong aria-hidden="true">33.</strong> 为何我们要与人类水平的表现作对比</a></li><li class="chapter-item expanded "><a href="chapter34.html"><strong aria-hidden="true">34.</strong> 如何定义人类水平的表现</a></li><li class="chapter-item expanded "><a href="chapter35.html"><strong aria-hidden="true">35.</strong> 超越人类水平表现</a></li><li class="chapter-item expanded "><a href="chapter36.html"><strong aria-hidden="true">36.</strong> 何时应该在不同的分布下训练和测试</a></li><li class="chapter-item expanded "><a href="chapter37.html"><strong aria-hidden="true">37.</strong> 如何决定是否使用所有数据</a></li><li class="chapter-item expanded "><a href="chapter38.html"><strong aria-hidden="true">38.</strong> 如何决定是否包含不一致的数据</a></li><li class="chapter-item expanded "><a href="chapter39.html"><strong aria-hidden="true">39.</strong> 加权数据</a></li><li class="chapter-item expanded "><a href="chapter40.html"><strong aria-hidden="true">40.</strong> 从训练集到开发集的泛化</a></li><li class="chapter-item expanded "><a href="chapter41.html"><strong aria-hidden="true">41.</strong> 识别偏差、方差和数据不匹配误差</a></li><li class="chapter-item expanded "><a href="chapter42.html"><strong aria-hidden="true">42.</strong> 处理数据不匹配</a></li><li class="chapter-item expanded "><a href="chapter43.html"><strong aria-hidden="true">43.</strong> 人工数据合成</a></li><li class="chapter-item expanded "><a href="chapter44.html"><strong aria-hidden="true">44.</strong> 优化验证测试</a></li><li class="chapter-item expanded "><a href="chapter45.html"><strong aria-hidden="true">45.</strong> 优化验证集的一般形式</a></li><li class="chapter-item expanded "><a href="chapter46.html"><strong aria-hidden="true">46.</strong> 强化学习样本</a></li><li class="chapter-item expanded "><a href="chapter47.html"><strong aria-hidden="true">47.</strong> 端到端学习的兴起</a></li><li class="chapter-item expanded "><a href="chapter48.html"><strong aria-hidden="true">48.</strong> 更多端到端学习示例</a></li><li class="chapter-item expanded "><a href="chapter49.html"><strong aria-hidden="true">49.</strong> 端到端学习的优点和缺点</a></li><li class="chapter-item expanded "><a href="chapter50.html"><strong aria-hidden="true">50.</strong> 选择流水线组件：数据可用性</a></li><li class="chapter-item expanded "><a href="chapter51.html"><strong aria-hidden="true">51.</strong> 选择流水线组件：任务简单</a></li><li class="chapter-item expanded "><a href="chapter52.html"><strong aria-hidden="true">52.</strong> 直接学习丰富的输出</a></li><li class="chapter-item expanded "><a href="chapter53.html"><strong aria-hidden="true">53.</strong> 组件错误分析</a></li><li class="chapter-item expanded "><a href="chapter54.html"><strong aria-hidden="true">54.</strong> 将错误归因于某个组件</a></li><li class="chapter-item expanded "><a href="chapter55.html"><strong aria-hidden="true">55.</strong> 错误归因的一般情况</a></li><li class="chapter-item expanded "><a href="chapter56.html"><strong aria-hidden="true">56.</strong> 组件错误分析和与人类水平的对比</a></li><li class="chapter-item expanded "><a href="chapter57.html"><strong 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<h1 class="menu-title">Machine Learning Yearning</h1>
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<h2 id="chapter-32plotting-learning-curves"><a class="header" href="#chapter-32plotting-learning-curves">Chapter 32、Plotting learning curves</a></h2>
<p><strong>绘制学习曲线</strong></p>
<p>假设你有一个非常小的训练集，只有100个样本。随机选择10个样本的子集来训练你的算法，然后是20个样本，然后30，直到100，以10个为间隔增加样本数。然后使用这10个数据点绘制学习曲线。你可能会发现曲线在较小的训练集大小下看起来有些嘈杂（意思是这些值比期望的要高/低）。</p>
<p>当只在10个随机选择的样本上训练时，你可能不幸选到了特别“bad”的训练集，例如有很多模棱两可/错误标注的样本。或者，你可能幸运的选到了特别“good”的训练集。小的训练集意味着开发和训练错误可能会随机波动。</p>
<p>如果你的机器学习应用严重偏倚一个类别（如负样本远比正样本多的猫分类任务），或者类别数比较大（如识别100种不同动物类别），那么选择尤其是“不具代表性”或坏的训练集的几率更大。例如，如果80%的样本是负样本（y=0），只有20%是正样本（y=1），那么有可能10个样本的训练集只包含负样本，因此很难让算法学习到有意义的东西。</p>
<p>如果训练曲线里的噪声使得很难看见真实的趋势，这里有两种解决方法：</p>
<ul>
<li>不是仅对10个样本的一个模型进行训练，而是通过从原始100个样本的数据集中通过替换的抽样方法【1】选择几个（如3-10）不同的随机选择的10个样本的训练集。在这些数据集上训练不同的模型，并对每个结果模型计算训练集和开发集错误。计算并绘制平均训练错误和平均开发集错误。</li>
<li>如果你的训练集比较倾向一种类别，或有很多类别，从100个训练样本中选择一个“平衡的”子集而不是随机选择的10个训练样本。例如，你可以确保2/10的样本是正样本，8/10为负样本。更为一般的说，你可以确保每个类别的样本部分尽可能的接近原始训练集的整体部分。</li>
</ul>
<p>我不会为这些技术而烦恼，除非你已经尝试过绘制学习曲线，并且认为曲线太嘈杂以至于看不到潜在的趋势。如果你的训练集较大（比如说超过1000个样本），并且你的类别分布不是很偏，你可能不需要这些技巧。</p>
<p>最后，绘制学习曲线可能花费很高的计算成本：例如，你可能需要训练10个模型，其中分别有1000个样本，然后是2000个，直到10000个。使用小的数据集训练模型比使用大数据集来训练模型要快的多。因此，不像上面那样均匀地将训练集大小按线性范围划分出来，你可以在1000、2000、4000、6000和10000个样本上训练模型。这样应该仍然可以让你清晰的了解学习曲线的趋势。当然，只有在训练所有附加模型的计算成本显著时，该方法才有意义。</p>
<p>————————————</p>
<p>【1】以下是采用替换的抽样方法（sampling with replacement）：你可以从100个里面随机选择10个不同的样本作为第一个训练集。然后你会再选10个样本，形成第二个训练集，不考虑第一个训练集中选了哪些样本。因此，一个特定的样本可能出现在第一和第二个训练集中。相反，如果你的样本没有被替换，第二个训练集将仅在第一次未被选择的90个样本中进行选择。在实践中，有或没有替换的抽样不应该产生很大的差异，但前者是常见的做法。</p>
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