# Shapley-PC: Constraint-based Causal Structure Learning with a Shapley Inspired Framework

arXiv: https://arxiv.org/abs/2312.11582 · HTML: https://mlsanity.com/paper/2312.11582/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 47 references that are in the map.
- First posted on arXiv 18 Dec 2023.

## Builds on (most cited first, 14 of 14)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [D'ya like DAGs? A Survey on Structure Learning and Causal Discovery](https://mlsanity.com/paper/2103.02582/) (2021)
- [Causal Inference and Causal Explanation with Background Knowledge](https://mlsanity.com/paper/1302.4972/) (2013)
- [Asymmetric Shapley values: incorporating causal knowledge into model-agnostic explainability](https://mlsanity.com/paper/1910.06358/) (2019)
- [Causal-learn: Causal Discovery in Python](https://mlsanity.com/paper/2307.16405/) (2023)
- [Causal Shapley Values: Exploiting Causal Knowledge to Explain Individual Predictions of Complex Models](https://mlsanity.com/paper/2011.01625/) (2020)
- [Learning Equivalence Classes of Bayesian Networks Structures](https://mlsanity.com/paper/1302.3566/) (2013)
- [Causal structure based root cause analysis of outliers](https://mlsanity.com/paper/1912.02724/) (2019)
- [A Survey on Causal Discovery: Theory and Practice](https://mlsanity.com/paper/2305.10032/) (2023)
- [The impact of prior knowledge on causal structure learning](https://mlsanity.com/paper/2102.00473/) (2021)
- [Constraint-Based Causal Discovery using Partial Ancestral Graphs in the presence of Cycles](https://mlsanity.com/paper/2005.00610/) (2020)
- [Improving Accuracy and Scalability of the PC Algorithm by Maximizing P-value](https://mlsanity.com/paper/1610.00378/) (2016)
- [ML4C: Seeing Causality Through Latent Vicinity](https://mlsanity.com/paper/2110.00637/) (2021)
- [SHAP-XRT: The Shapley Value Meets Conditional Independence Testing](https://mlsanity.com/paper/2207.07038/) (2022)

## Abstract (arXiv)

Causal Structure Learning (CSL), also referred to as causal discovery, amounts to extracting causal relations among variables in data. CSL enables the estimation of causal effects from observational data alone, avoiding the need to perform real life experiments. Constraint-based CSL leverages conditional independence tests to perform causal discovery. We propose Shapley-PC, a novel method to improve constraint-based CSL algorithms by using Shapley values over the possible conditioning sets, to decide which variables are responsible for the observed conditional (in)dependences. We prove soundness, completeness and asymptotic consistency of Shapley-PC and run a simulation study showing that our proposed algorithm is superior to existing versions of PC.