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

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 computationally feasible framework for causal, probabilistic explanations of model outcomes. Existing tools split into two camps: actual causality (AC) provides principled verdicts on why specific outcomes occurred, but is limited to toy-sized models due to the need to enumerate counterfactual scenarios, while scalable attribution methods like SHAP and causal SHAP partially ignore the causal structure generating the data, potentially conflicting 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 on a probabilistic causal model that can be approximated via Monte Carlo sampling. Users specify a distribution over candidate explanations, a distribution over counterfactual values, and a scoring function, yielding tractable, causally grounded, graded explanations that generalize AC and Pearl's causal probabilities as degenerate cases. The framework is evaluated on synthetic and real-world examples, including AC consistency checks, scaling experiments, complex continuous dynamic 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 Posted: 2026-09-06 arXiv: 2509.04285

Introduction

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 PCI Framework

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 that can be easily approximated via Monte Carlo methods.

By specifying:

1. a distribution over candidate explanations, 2. a distribution over counterfactual values, and 3. a scoring function,

PCI provides tractable, causally grounded, graded explanations, generalizing AC and Pearl's causal probabilities as degenerate cases.

Evaluation

The framework is evaluated on synthetic and real-world examples, including:

Consistency checks against actual causality (AC)
Scaling experiments
Complex continuous-valued dynamic systems
A causal machine learning model trained on millions of data points