Probabilistic Causal Impact (PCI): A Computationally Feasible Framework for Causal Probabilistic Explanation

Forum topic · 小凯 · 2026-09-07

Summary

This arXiv paper (2509.04285) by Rafal Urbaniak, Sam Witty, and Daniel Waxman introduces Probabilistic Causal Impact (PCI), a framework for explaining why specific outcomes occur and which inputs deserve blame or credit. Existing approaches split into two camps: actual causality (AC) theory offers principled verdicts but only works on toy models due to the need to enumerate counterfactual scenarios, while scalable attribution methods like SHAP and causal SHAP partially ignore the data's causal structure and may conflict with careful causal analysis. PCI bridges this gap by building on actual causality and Pearl's probability of necessity and sufficiency, recasting explainability as an estimation problem over probabilistic causal models that can be approximated via Monte Carlo methods. By specifying a distribution over candidate explanations, counterfactual value distributions, and a scoring function, PCI delivers tractable, causally grounded, graded explanations that generalize AC and Pearl's causal probabilities as degenerate cases. The authors evaluate PCI on synthetic and real-world examples, including consistency checks against AC, scaling experiments, complex continuous-valued dynamical systems, and a causal machine learning model trained on millions of data points.

Paper Overview

Field: Machine Learning Authors: Rafal Urbaniak, Sam Witty, Daniel Waxman Published: 2026-09-06 arXiv: 2509.04285

Abstract (Full Translation)

Explaining why a specific outcome occurred, and which inputs deserve the blame or credit, is central to philosophical, scientific, and policy analysis. Existing tools split into two camps. The theory of actual causality (AC) gives principled verdicts, but only for toy-sized models, because computing them requires enumerating counterfactual scenarios. Scalable attribution methods like SHAP (or even causal SHAP) at least partially ignore the causal structure that generated the data, and can give answers that conflict with a careful causal analysis.

We close this gap with Probabilistic Causal Impact (PCI). PCI builds on actual causality and on Pearl's notions of probability of necessity and sufficiency, but recasts the question of explainability as an estimation problem on a probabilistic causal model, which can be easily approximated via Monte Carlo. By specifying a distribution over candidate explanations, a distribution over counterfactual values, and a scoring function, PCI provides tractable, causally grounded, graded explanations that generalize actual causality and Pearl's probabilities of causation as degenerate cases.

We evaluate PCI on synthetic and real-world examples, including consistency checks against AC, scaling experiments, complex continuous-valued dynamical systems, and a causal machine learning model trained on millions of data points.

Key Contributions

Bridges two research camps: connects principled but intractable actual causality theory with scalable but causally shallow attribution methods like SHAP
Monte Carlo estimation: reframes explainability as a tractable estimation problem on probabilistic causal models
Generalizes prior notions: actual causality and Pearl's probability of necessity/sufficiency emerge as degenerate cases of PCI
Empirical evaluation: validated on AC consistency checks, scaling tests, continuous dynamical systems, and a large-scale causal ML model trained on millions of data points

---

*Auto-collected on 2026-09-07*