mlsanityData to 7 Oct 2026

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

arXiv 1502.02454 ↗First posted 9 Feb 2015cs.AIcited by 45

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Abstract (arXiv)

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.

Key facts. Cited by 45 papers in the map (data through 7 Oct 2026). First posted on arXiv 9 Feb 2015.

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Citing papers per year: 2019: 1; 2020: 0; 2021: 9; 2022: 4; 2023: 5; 2024: 11; 2025: 9; 2026: 6.

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  1. 2019Causal Confusion in Imitation Learningcited by 286
  2. 2021D'ya like DAGs? A Survey on Structure Learning and Causal Discoverycited by 209
  3. 2023A Survey on Causal Discovery: Theory and Practicecited by 63
  4. 2021gCastle: A Python Toolbox for Causal Discoverycited by 60
  5. 2023pgmpy: A Python Toolkit for Bayesian Networkscited by 21
  6. 2021Object-Aware Regularization for Addressing Causal Confusion in Imitation Learningcited by 16
  7. 2022Causal Discovery for Fairnesscited by 16
  8. 2023Learning for Counterfactual Fairness from Observational Datacited by 13
  9. 2024Recursive Causal Discoverycited by 12
  10. 2021Data-driven discovery of interpretable causal relations for deep learning material laws with uncertainty propagationcited by 10
  11. 2023CDANs: Temporal Causal Discovery from Autocorrelated and Non-Stationary Time Series Datacited by 7
  12. 2024Causal Discovery in Semi-Stationary Time Seriescited by 7
33 more
  1. 2022Granger Causal Chain Discovery for Sepsis-Associated Derangements via Continuous-Time Hawkes Processescited by 6
  2. 2024COKE: Causal Discovery with Chronological Order and Expert Knowledge in High Proportion of Missing Manufacturing Datacited by 5
  3. 2024Root Cause Attribution of Delivery Risks via Causal Discovery with Reinforcement Learningcited by 5
  4. 2024Large-Scale Targeted Cause Discovery via Learning from Simulated Datacited by 5
  5. 2021Partitioned hybrid learning of Bayesian network structurescited by 4
  6. 2021Causal Inference in medicine and in health policy, a summarycited by 4
  7. 2024Causal Discovery over High-Dimensional Structured Hypothesis Spaces with Causal Graph Partitioningcited by 4
  8. 2024Causal Inference with Latent Variables: Recent Advances and Future Prospectivescited by 4
  9. 2021A Fast PC Algorithm with Reversed-order Pruning and A Parallelization Strategycited by 3
  10. 2022Fast Parallel Bayesian Network Structure Learningcited by 3
  11. 2025Learning Identifiable Structures Helps Avoid Bias in DNN-based Supervised Causal Learningcited by 3
  12. 2021The Dual PC Algorithm and the Role of Gaussianity for Structure Learning of Bayesian Networkscited by 2
  13. 2024Fast-PGM: Fast Probabilistic Graphical Model Learning and Inferencecited by 2
  14. 2025Causality Is Key to Understand and Balance Multiple Goals in Trustworthy ML and Foundation Modelscited by 2
  15. 2025A Fast Kernel-based Conditional Independence test with Application to Causal Discoverycited by 2
  16. 2025Robust Causal Discovery under Imperfect Structural Constraintscited by 2
  17. 2022Improving the Efficiency of the PC Algorithm by Using Model-Based Conditional Independence Testscited by 1
  18. 2023Causal Graph Discovery from Self and Mutually Exciting Time Seriescited by 1
  19. 2025Less Greedy Equivalence Searchcited by 1
  20. 2026Trustworthy AI Suffers from Invariance Conflicts and Causality is The Solutioncited by 1
  21. 2021Causal Graph Discovery from Self and Mutually Exciting Time Seriescited by 0
  22. 2024Inference of Causal Networks using a Topological Thresholdcited by 0
  23. 2024Learning linear acyclic causal model including Gaussian noise using ancestral relationshipscited by 0
  24. 2024Scalable Time-Series Causal Discovery with Approximate Causal Orderingcited by 0
  25. 2025Symmetric observations without symmetric causal explanationscited by 0
  26. 2025Causality-Induced Positional Encoding for Transformer-Based Representation Learning of Non-Sequential Featurescited by 0
  27. 2025Integrating Causal Inference with Graph Neural Networks for Alzheimer's Disease Analysiscited by 0
  28. 2025Scalable Bayesian Network Structure Learning Using Tsetlin Machine to Constrain the Search Spacecited by 0
  29. 2026Efficient Causal Structure Learning via Modular Subgraph Integrationcited by 0
  30. 2026A Recursive Decomposition Framework for Causal Structure Learning in the Presence of Latent Variablescited by 0
  31. 2026On the Recoverability of Causal Relations from Bulk Gene Expression Datacited by 0
  32. 2026polyDAG: Polynomial Acyclicity Constraints for Efficient Continuous Causal Discovery in Visual Semantic Graphscited by 0
  33. 2026Conditional Independence Tests for Constraint-Based Causal Discovery: A Surveycited by 0