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

Overview

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

Summary

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:

• 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.

The authors 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 methods.

By specifying a distribution over candidate explanations, a distribution over counterfactual values, and a scoring function, PCI provides tractable, causally grounded, graded explanations — generalizing AC and Pearl's causal probability as degenerate cases.

Evaluation

PCI was evaluated on synthetic and real-world examples, including:

• Agreement tests with actual causality verdicts
• Scaling experiments
• Complex continuous-valued dynamical systems
• A causal machine learning model trained on millions of data points

Links

• Paper: arxiv.org/abs/2509.04285