The Clique-Picking Algorithm

This repository countains multiple implementations of the Clique-Picking algorithm that we have proposed at AAAI 2021 [1] for counting the number of Markov equivalent DAGs in polynomial time. Moreover, we give implementations of the polynomial-time algorithm for uniformly sampling a DAG from a Markov Equivalence Class, which we refined in [2]. See also chapter 5 of my thesis [3].

1. Marcel Wienöbst, Max Bannach, and Maciej Liśkiewicz: Polynomial-Time Algorithms for Counting and Sampling Markov Equivalent DAGs (AAAI 2021) arXiv version
2. Marcel Wienöbst, Max Bannach, and Maciej Liśkiewicz: Polynomial-Time Algorithms for Counting and Sampling Markov Equivalent DAGs with Applications (JMLR)
3. Marcel Wienöbst: Algorithms for Markov Equivalence (PhD Thesis)

Implementations

We provide the following implementations:

• aaai_experiments/ contains the original C++ implementation and experiments from the AAAI 2021 conference paper (only counting is implemented here)
• cliquepicking_julia/ contains the subsequent Julia code additionally provides a sampling algorithm
• cliquepicking_rs/ contains a recent Rust implementation for counting and sampling, which is cleaner and slightly more efficient (worst-case n^3)
• cliquepicking_python/ contains a Python wrapper for the Rust implementation. You can install and use the Python implementation easily via pip install cliquepicking.

Brief examples of how to install and use the implementations are given in the subdirectories.