Hierarchical Causal Abduction: A Foundation Framework for Explainable Model Predictive Control

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 that is 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, generalizing AC and Pearl's probability of causation as degenerate cases. We evaluate PCI in synthetic and real-world examples, spanning consistency checks with AC, scaling experiments, complex continuous-valued dynamical systems, and a real-world deployed causal machine learning model trained on millions of datapoints.

Explaining the predictions of neural networks is a central challenge in trustworthy AI. Existing explanation methods, such as those based on feature attribution or minimal sufficient sets, typically treat input features as independent, which can yield misleading explanations when inputs exhibit structured dependencies. We address this by formalizing explanations as Halpern-Pearl (HP) actual causes, modeling input dependencies using Boolean Structural Causal Models (SCMs). We compute HP causes by applying bound propagation and branch-and-bound techniques, while providing formal guarantees of completeness and minimality. Our experiments show that we substantially outperform brute-force and ILP baselines in scalability, and outperform heuristic search as graph size grows, computing all minimal actual causes on instances with search spaces of up to $2.3\times10^{13}$ candidate (cause, contingency) pairs, on SCMs with up to 28 nodes, within a 180s per-instance budget. In a case study, we further show that ignoring input dependencies inflates the number of reported causes, 14.9% of which are spurious under our SCM.

Causal Discovery (CD) from observational data faces two fundamental challenges. First, purely statistical methods often lack the power to resolve structural ambiguities in low-sample regimes. Second, although LLM-assisted hybrid approaches improve structure recovery through semantic reasoning, the influence of that reasoning on individual edge decisions remains largely opaque. Consequently, existing hybrid methods fail to satisfy a fundamental requirement: explaining why a particular edge is included or excluded in the learned directed acyclic graph (DAG). This is critical in real-world applications, where no ground-truth DAG exists and every structural decision must be independently justified. We formalize this requirement as decision traceability, requiring every inferred edge to be supported by auditable statistical evidence, Markov Blanket consistency, or explicit domain reasoning. We propose GENESIS, an explainable hybrid CD framework that decomposes graph construction into interpretable decision points. GENESIS first identifies and scores three-node structural motifs, including chains, forks, and colliders, to establish transparent structural priors, then progressively refines the graph by integrating these priors with observational evidence, invoking domain knowledge only when statistical evidence is insufficient. By design, every edge decision is resolved through an auditable source of evidence. Experiments show that GENESIS achieves 100% decision traceability across all settings, establishing explainability as a first-class objective in causal discovery. Despite this additional requirement, GENESIS consistently outperforms purely statistical CD methods on the majority of benchmark datasets across all sample regimes in terms of Structural Hamming Distance (SHD), while achieving performance comparable to state-of-the-art LLM-assisted approaches.