This repository contains a Python implementation of the original PC algorithm, as described in Causation, Prediction, and Search by P. Spirtes, C. Glymour and R. Scheines (2nd edition, MIT Press, 2000).
The package is available from PyPi : PyPCAlg.
To install, run
pip install PyPCAlg
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).
from PyPCAlg.pc_algorithm import run_pc_algorithm, field_pc_cpdag, \
field_separation_sets
from PyPCAlg.examples.graph_4 import generate_data
from PyPCAlg.examples.graph_4 import oracle_indep_test
from PyPCAlg.examples.graph_4 import oracle_cond_indep_test
from PyPCAlg.examples.graph_4 import get_adjacency_matrix
df = generate_data(sample_size=10)
independence_test_func = oracle_indep_test()
conditional_independence_test_func = oracle_cond_indep_test()
dic = run_pc_algorithm(
data=df,
indep_test_func=independence_test_func,
cond_indep_test_func=conditional_independence_test_func,
level=0.05
)
cpdag = dic[field_pc_cpdag]
separation_sets = dic[field_separation_sets]
print(f'The true causal graph is \n{get_adjacency_matrix()}')
print(f'\nThe CPDAG retrieved by PC is \n{cpdag}')The example above demonstrates the use of the PC algorithm on one of the examples provided, using oracle independence and conditional independence tests. The user can provide their own tests of independence / conditional independence ; they need only have the following signatures :
def user_provided_independence_test(data: pandas.DataFrame, x: int, y: int,
level: float) -> bool:
"""
Tests whether the variables X and Y with respective observations
data.iloc[:, x] and data.iloc[:, y] are statistically independent at
the level considered
"""
# code for the independence test provided by the user goes here...
def user_provided_conditional_independence_test(data: pandas.DataFrame, x: int,
y: int, z: list[int], level: float) -> bool:
"""
Tests whether the variables X and Y with respective observations
data.iloc[:, x] and data.iloc[:, y] are statistically independent
conditionally on the variables z with observations data.iloc[:, z] at
the level considered.
"""
# code for the conditional independence test provided by the user goes here...- Causation, Prediction, and Search P. Spirtes, C. Glymour and R. Scheines (2nd edition, MIT Press, 2000)
@book{SpirtesGlymourScheines2000,
author = {Spirtes, Peter and Glymour, Clark N and Scheines, Richard},
title = {{Causation, Prediction, and Search}},
publisher = {MIT press},
year = {2000},
edition = {2nd},
series = {Adaptive Computation and Machine Learning}
}