PyPCAlg

This repository contains a Python implementation of the original PC algorithm.

Structure of the package

Folder examples contains examples of small dimensional graphs (i.e. with a low number of nodes) to test the PC algorithm on.

The exhaustive lists of the (conditional) independence relationships satisfied by these examples (assuming both the causal Markov condition and causal Faithfulness) have been worked out. They are contained in files :

• examples/true_independence_relationships_graph_1.csv,
• examples/true_independence_relationships_graph_2.csv,
• examples/true_independence_relationships_graph_3.csv, and
• examples/true_independence_relationships_graph_4.csv.

In practice, the results of the PC algorithm depend on the statistical tests of (conditional) independence that we use. Considering the high number of statistical (conditional) independence tests carried out by the PC algorithm (even on graphs of moderate sizes), it is inevitable that some of these statistical tests will be erroneous (that is the whole problem of Multiple Hypothesis Testing).

By providing the lists of (conditional) independence relationships satisfied by the examples, we make it possible to check whether the implementation of the PC algorithm itself is correct (indeed, things are as if we had at our disposal statistical tests of unconditional/conditional dependence that always return a correct result : no type I error, no type II error).