Explaining why a particular outcome occurred and which inputs deserve blame or credit is central to philosophy, science, and policy analysis. Existing tools fall into two camps: the theory of actual causality (AC) provides principled verdicts but only for toy‑sized models because it requires enumerating all counterfactual scenarios; scalable attribution methods such as SHAP (and causal SHAP) often ignore the causal structure that generated the data and can produce answers that conflict with a careful causal analysis.
We close this gap with Probabilistic Causal Impact (PCI). PCI builds on AC and on Pearl’s notions of probability of necessity $P(N)$ and probability of sufficiency $P(S)$, but recasts explainability as an estimation problem on a probabilistic causal model that can be approximated efficiently via Monte Carlo simulation. The procedure is: (1) specify a distribution over “candidate explanations”; (2) generate a distribution over counterfactual values for each candidate; (3) define a scoring function $\text{score}(e)=\mathbb{E}[\text{impact}\mid e]$ that quantifies the causal contribution of an explanation.
Under this framework, AC and Pearl’s probability of causation appear as degenerate cases of PCI: when the candidate set contains a single variable and the scoring function takes an extreme limit, PCI’s output collapses to the traditional deterministic causality verdict.
We evaluate PCI on synthetic and real‑world examples, covering consistency checks with AC, scaling experiments, complex continuous‑valued dynamical systems, and a deployed causal machine‑learning model trained on millions of datapoints. The results demonstrate that PCI retains causal rigor while offering substantial computational feasibility.
Review