A fast PC algorithm for high dimensional causal discovery with multi-core PCs

TL;DR

This paper introduces parallel-PC, a multi-core CPU optimized algorithm that significantly accelerates high-dimensional causal discovery, making it feasible on personal computers and improving both efficiency and accuracy.

Contribution

The paper presents a parallelized version of the PC algorithm that is memory-efficient and suitable for multi-core PCs, enabling high-dimensional causal discovery within practical timeframes.

Findings

Parallel-PC reduces runtime from over 24 hours to less than 12 hours on a 4-core CPU.

Parallel-PC completes analysis within 6 hours on an 8-core CPU.

Using parallel-PC improves the accuracy of causal inference in high-dimensional datasets.

Abstract

Discovering causal relationships from observational data is a crucial problem and it has applications in many research areas. The PC algorithm is the state-of-the-art constraint based method for causal discovery. However, runtime of the PC algorithm, in the worst-case, is exponential to the number of nodes (variables), and thus it is inefficient when being applied to high dimensional data, e.g. gene expression datasets. On another note, the advancement of computer hardware in the last decade has resulted in the widespread availability of multi-core personal computers. There is a significant motivation for designing a parallelised PC algorithm that is suitable for personal computers and does not require end users' parallel computing knowledge beyond their competency in using the PC algorithm. In this paper, we develop parallel-PC, a fast and memory efficient PC algorithm using the parallel computing technique. We apply our method to a range of synthetic and real-world high dimensional datasets. Experimental results on a dataset from the DREAM 5 challenge show that the original PC algorithm could not produce any results after running more than 24 hours; meanwhile, our parallel-PC algorithm managed to finish within around 12 hours with a 4-core CPU computer, and less than 6 hours with a 8-core CPU computer. Furthermore, we integrate parallel-PC into a causal inference method for inferring miRNA-mRNA regulatory relationships. The experimental results show that parallel-PC helps improve both the efficiency and accuracy of the causal inference algorithm.