Causal Explanation

Model explainability is essential for understanding and trusting machine learning models. Existing explainable AI methods often explain predictions through feature importance, counterfactual explanations, or rules. However, a region-level characterization of when and only when a prediction behavior arises remains less explored. This paper proposes Causal Sufficient and Necessary Regional Explanations (SNRE), a framework that learns an input region $A$ and output region $B$ such that membership in $A$ is both sufficient and necessary for the model output to fall in $B$. Motivated by the classical Probability of Necessity and Sufficiency (PNS), we formulate a region-level PNS measure through stochastic interventions and derive a differentiable finite-sample estimator for optimization. SNRE parameterizes the input-output region pair with explicit and interpretable algebraic region families, together with a learnable feature mask, balancing expressiveness and interpretability. Experiments demonstrate that SNRE learns region pairs with strong sufficiency-necessity performance, robust explanation behavior, and practical utility for model analysis.

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.

Causal discovery aims to uncover the underlying causal relationships given data generated from a system. The goal, however, is not merely to predict causal edges given data, but also to be able to interpret and explain either observed or hypothesized phenomena, such as a particularly large causal effect. We consider this task of conditional causal discovery and cast it as a Bayesian inference problem, in which we target the posterior over causal graphs and parameters conditional on an event such as a causal-effect constraint. Unfortunately, this poses a computational challenge: existing approaches to Bayesian causal discovery struggle when the event has small posterior mass. To address this, we adapt rare-event estimation techniques to perform inference the joint graph-parameter space. Our method gradually drives a particle population toward the constrained region while maintaining samples that approximate the conditional posterior. Empirical evaluation on synthetic graphs validates the accuracy of our approach at small and large scales, and we show in a case study on the Sachs protein dataset how our method can be used to aid scientific exploration by providing pathway-level summaries.

Predictive explanation methods attribute a model output; they do not, by themselves, attribute an intervention effect on the real-world outcome. We introduce the Causal Attribution Score (CAS), a compact score architecture for causal explanation. CAS starts from an identified interventional coalition game, allocates the joint intervention contrast with causal Shapley contributions, and converts those raw outcome-scale effects into Local CAS, Signed Local CAS, and two complementary Global CAS summaries. The innovation is not a new Shapley formula, but a local-to-global causal reporting layer with an explicit intervention target. In the known-truth benchmark, eight repeated primary-interaction simulations (n = 2,200 each, three actions) gave mean Local CAS MAE of 0.107 for coalition-aware CAS, compared with 0.173 for one-at-a-time normalisation and 0.213 for a global normalised absolute ATE vector. The paired advantage over one-at-a-time normalisation increased from -0.003 under additivity to 0.091 under strong interactions. On both empirical DoubleML datasets, 401(k) eligibility/net financial assets (n = 9,915) and Pennsylvania reemployment bonus/unemployment duration (n = 5,099), predictive SHAP/TreeSHAP rankings differed materially from Feature-CAS rankings of treatment-effect modifiers. In Pennsylvania, dep1 (exactly one dependent) moved from predictive global rank 13 to Feature-CAS rank 2 and was the leading local Feature-CAS modifier. These results isolate the added value of separating what predicts the outcome from what explains heterogeneity in an estimated causal effect.

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.

Abductive reasoning operates in two directions. The synthetic mode builds explanations from available hypotheses; the analytic mode, conversely, identifies the latent factors whose interaction accounts for a complex observed state. This paper develops the analytic mode as a non-greedy, risk-sensitive discipline of commitment, in which candidate factors coexist and interact, resolving into committed conclusions only when explicit governance conditions are met. The formal core is the $κ$-$τ$ apparatus: $κ$ encodes the epistemic interaction among hypotheses, and $τ$ sets a commitment threshold calibrated to the decision's stakes. The central contribution is the causal cluster, a structured object recording which latent factors participate in a decomposition, with what weights and interaction structure, together with a two-level architecture (intra-cluster $κ^*$, inter-cluster $κ^{**}$) that guards against causal misattribution. Demonstrated in epidemiological crisis decomposition and adversarial cyber threat analysis, the framework's contribution to human-AI reasoning is the legibility of suspended decomposition as a shared coordination object, providing structural resistance to premature convergence. In practice, the decision-maker is handed not a single imposed answer but the competing explanatory scenarios, weighted by plausibility and paired with the evidence that would resolve between them, so that sound action is possible even before the ambiguity is resolved.

This paper addresses Carl Hempel's longstanding problem of statistical ambiguity in inductive-statistical inference, in which contradictory predictions are derived from statistical laws. To avoid such predictions, Carl Hempel proposed the Requirement of Maximal Specificity (RMS) for the statistical laws used in the inference. An analysis of the RMS refinements made by Wesley Salmon, Alberto Coffa, and James Fetzer led to the following definition of maximally specific statistical laws: "the lawlike premises of an adequate explanation must specify all and only those properties whose presence or absence made a difference to the occurrence of its explanandum-phenomenon." However, there was no proof of a solution to the statistical ambiguity problem based on this definition. We use Nancy Cartwright's definition of causes that raise probabilities across background contexts, and then introduce the concept of Causal Rules. Then we define a special semantic probabilistic inference procedure that incrementally refines these causal rules by incorporating all statistically relevant information. This procedure yields Maximally Specific Causal Relationships (MSCRs), for which we prove (Theorem 1) that predictions derived from them are consistent. This resolves the statistical ambiguity problem. The semantic probabilistic inference procedure provides a probabilistic causal learning system, which may be used in such new areas as Causal AI and Causal Machine Learning. They fundamentally explore causal inference as a tool for understanding cause-and-effect relationships within complex systems. Properties similar to RMS remain under discussion. Several notions related to RMS are considered: invariant feature learning, invariant causal prediction, and spurious association.

Interpretable explanation methods in Artificial Intelligence aim to uncover the underlying causes and their effects, enabling a deeper understanding of why a system behaves in a certain way under different inputs. Unlike traditional explainability methods, which mainly highlight correlations between input and output variables, causal explanation focuses on interventional questions. By doing so, it provides more robust insights, helping users understand automated decisions, especially in high-risk domains. Recovering an explicit directed causal structure, however, is often impractical in large-scale, hybrid cyber-physical systems with feedback loops and partial observability. This paper introduces a novel framework inspired by statistical mechanics that instead models variable dependencies through an undirected, energy-based representation of cyber-physical IoT systems. Our approach enables rigorous dependency-aware attribution by analysing how variations in the energy landscape reflect the influence of individual components, without recovering a directed causal graph. It also supports reasoning about perturbation effects across hybrid interactions, providing reliable explanations of abnormal behaviours. We empirically examined our framework through simulations on an industrial IoT testbed with hybrid continuous and discrete variables, demonstrating higher attribution accuracy, improved robustness and better scalability than state-of-the-art graph-based approaches. While the attributions are not intended to fully recover the system's generative dynamics, they provide valuable, dependency-aware explanations supporting both human interpretation and downstream predictive and diagnostic tasks. Although demonstrated in industrial IoT security, our framework also applies to other high-dimensional cyber-physical and socio-technical systems requiring principled, structural explanations.

A central goal of science is to produce valid explanations of complex systems: high-level causal accounts that faithfully reflect the behavior of lower-level mechanisms. Yet no consensus exists on how to measure whether a proposed high-level explanation is actually valid. We introduce a benchmark of ten complex systems spanning both discrete and continuous state spaces, as well as static and dynamical regimes, each equipped with consensual ground-truth causal explanations and invalid contrastive conditions. Within a unified causal abstraction framework, we systematically evaluate over thirty candidate metrics drawn from observational, functional, information-theoretic, and causal families. Our results show that only the latter reliably discriminates valid from invalid abstractions, and only when incorporating faithfulness testing over unmapped variables. Building on these findings, we introduce the Causal Abstraction Error (CAE), a continuous validity metric with an explicit faithfulness test, which passes all discrimination tests across every system and can converge with as few as 30 sampled interventions. We offer it as a general-purpose metric for the discovery and validation of high-level explanations.

Modern autonomous Cyber-Physical Systems (CPSs), such as self-driving cars, face increasingly complex demands, and yet are expected to act reliably. The black-box nature often characterizing such systems, especially those relying on neural components, makes it impossible to fully verify the system behavior prior to deployment. Unfortunately, unexpected failures-when the system does not comply with its specification-are inevitable and may have catastrophic implications. To improve trust in the system and facilitate future mitigation after a failure occurs, it is important to try to derive an explanation for the unexpected system behavior. This paper introduces the novel concept of leveraging the framework of actual causality for CPS failure explanation. Up until now, this framework was only used to derive explanations in the context of simple systems, such as image classifiers. This paper addresses the theoretical gaps and provides the guidance needed to allow for correct explanation derivation in the CPS domain. Beyond the theoretical contribution, the paper presents two novel, practical, system-agnostic explanation derivation algorithms, allowing to prioritize either explanation optimality or derivation efficiency. The approach is demonstrated and evaluated in the context of a neural-network-controlled autonomous car, designed to avoid collisions.

Lane-change prediction is a central task in intelligent vehicles, where early maneuver anticipation can support safer decision-making. However, many existing approaches mainly learn statistical associations between observed driving variables and future maneuvers, while overlooking the causal dependencies among the input variables themselves. This limits interpretability, especially when physically related variables such as longitudinal gap, relative longitudinal velocity, and Time-To-Collision (TTC) are treated as independent flat inputs. This article presents a causal-inference-based framework for lane-change prediction and explanation. The proposed approach combines linguistic feature construction, expert-constrained causal discovery, deep structural causal modeling with Deep End-to-end Causal Inference (DECI), intervention-based effect analysis, refutation testing, and recursive causal-chain explanation. The objective is not only to predict the future maneuver, but also to identify candidate variables that directly contribute to the prediction, the upstream factors influencing them, and the causal chains through which these effects propagate. The framework achieves average F1-scores above 95% during the first three seconds before the lane-marking crossing event. Beyond prediction accuracy, the framework uses intervention-based effect analysis to distinguish influential from weakly influential variables under the learned causal structure. It further distinguishes candidate direct contributors from mediated effects and generates contrastive causal-chain explanations that clarify why the predicted maneuver is favored and why the alternative maneuvers are less supported. The main contribution is therefore a mechanism-aware lane-change prediction pipeline that moves beyond correlation-based classification toward more interpretable causal reasoning for maneuver prediction.

Building on recent formalizations of root cause analysis for rare events (``outliers'') in structural equation models, we propose a formal definition of a causal pathway and discuss its testable implications. We identify conditions under which these implications depend only on a causal abstraction defined by the pathway of rare events, rather than on the full causal graph of the underlying system. Accordingly, we introduce an abstraction of causal structure to pathways of rare events that bridges simple verbal causal explanations and detailed causal modeling.

Emotion-Cause Pair Extraction (ECPE) was introduced to explain why an emotion occurs, but this goal is now often reduced to binary pair/non-pair prediction. This proxy is useful for direct-cause extraction, yet easy to over-read as evidence grounded emotion explanation. We show that this interpretation is only partially valid. In IEMO-MECP, 90.9% of original positives remain emo-cause and 95.0% of original negatives remain non-pair, confirming that the binary ECPE task is largely preserved. The problem is that direct triggers alone do not constitute a grounded explanation. Emo-context, an utterance that helps interpret a target emotion without directly causing it, appears on both sides of the original boundary and is enriched near binary uncertainty, showing that the binary boundary has no stable place for such discourse evidence. Across evaluated ECPE models, direct triggers are recovered more reliably than contextual support. Under shortcut pressure, this imbalance becomes consequential. Binary-trained models assign higher pair scores to nearby lexically similar non-pair candidates than to evidence supported but structurally harder emo-cause and emo-context pairs. Thus, pair scores can reward convenient attributions over grounded explanations. High binary ECPE performance indicates that a model can identify direct triggers; it does not indicate that the model has explained the emotion. Code is publicly available at https://github.com/panzhzh/ECPExsame.

Explainable AI (XAI) methods identify which features are relevant to a model's predictions but often fail to clarify why certain decisions are made. In this work, we present a novel method that integrates causality with argument-based reasoning to explain why models may be making predictions. Our approach first identifies causal relationships among variables using causal discovery methods and then translates these into a Bipolar Argumentation Framework (BAF) to represent supportive and opposing interactions among features. By using semi-stable semantics, we find extensions of features that explain why certain outcomes may have been chosen. We demonstrate our method on two benchmark datasets and compare its results against standard post-hoc explainability approaches.

Large language models (LLMs) can generate high-level diverse phenomena without explicitly programmed rules. This capability has led to their adoption within different agent-based models (ABMs) and social simulations. Recent studies investigate their ability to generate different phenomena of interest, for example, human behavior on social media platforms or alien behavior in game-theoretic scenarios. However, capability, prediction, and explanation are different--drawing from the philosophy of science and mechanisms literature, explanation requires showing, to some degree, how a phenomenon is produced by related organized entities and activities. For modelers, describing the characteristics of an experiment or whether a simulation provides progress in capability (or explanation), can be difficult without being grounded in potentially distant research areas. We integrate recent work on LLM-ABMs with contemporary philosophy of science literature and use it to operationalize a definition of 'plausibility' in a four-level scale. Our scale separates the evaluation of a model's generative sufficiency (ability to reproduce a phenomenon) from its mechanistic plausibility (how the phenomenon could be produced), and clarifies the distinct roles of different models, such as predictive and explanatory ones. We introduce this as the Mechanism Plausibility Scale.

Model Predictive Control (MPC) is widely used to operate safety-critical infrastructure by predicting future trajectories and optimizing control actions. However, nonlinear dynamics, hard safety constraints, and numerical optimization often render individual control moves opaque to human operators, undermining trust and hindering deployment. This paper presents Hierarchical Causal Abduction (HCA), which combines (i) physics-informed reasoning via domain knowledge graphs, (ii) optimization evidence from Karush--Kuhn--Tucker (KKT) multipliers, and (iii) temporal causal discovery via the PCMCI algorithm to generate faithful, human-interpretable explanations for control actions computed by nonlinear MPC. Across three diverse control applications (greenhouse climate, building HVAC, chemical process engineering) with expert validation, HCA improves explanation accuracy by 53% over LIME (0.478 vs. 0.311) using a single set of cross-domain parameters without per-domain tuning; domain-specific KKT-threshold calibration over 2--3 days further increases accuracy to 0.88. Ablation studies confirm that each evidence source is essential, with 32--37% accuracy degradation when any component is removed, and HCA's ranking-and-validation methodology generalizes beyond MPC to other prediction-based decision systems, including learning-based control and trajectory planning.

Neural networks have proved an effective means of learning control policies for autonomous systems, but these learned policies are difficult to understand due to the black-box nature of neural networks. This lack of interpretability makes safety assurance for such autonomous systems challenging. The fields of eXplainable Artificial Intelligence (XAI) and eXplainable Reinforcement Learning (XRL) aim to interpret the decision making processes of neural networks and autonomous agents, respectively. In particular, work on causal explanations aims to provide "why" and "why not" explanations for why a model made a given decision. However, most of the work on explainability to date utilises a distilled version of the original model. While this distilled policy is interpretable, it necessarily degrades in performance significantly when compared to the original model, and is not guaranteed to be an accurate reflection of the decision making processes in the original model and as such cannot be used to guarantee its safety. Recent work on understanding the geometry of ReLU neural networks shows that a ReLU network corresponds to a piecewise linear function divided into regions defined by an n-dimensional convex polytope. Through this lens, a neural network can be understood as dividing the input space into distinct regions which apply a single linear function for each output neuron. We show that this geometric representation can be used to generate causal explanations for the network's behaviour similar to previous work, but which extracts rules directly from the geometry of Neural Networks with the ReLU activation function, and is therefore an accurate reflection of the network's behaviour.

We establish, from the point of view of Explainable AI (XAI), connections between Consistency-Based Diagnosis (CBD), on one side, and Actual Causality and Causal Responsibility, on the other. CBD has received little attention from the XAI community. Connections between these two areas could have a fruitful impact on XAI and Explainable Data Management.

Why do some physical systems possess consciousness, while others do not? A scientific theory of consciousness must explain differences in system behavior in terms of well-defined internal mechanisms. However, many existing approaches introduce higher-level structural or informational descriptions without specifying how these structures contribute to the generation of behavior, raising the concern that they may become theoretically ineffective.A further difficulty arises from the status of causation. Attempts to introduce causally effective mental states appear to conflict with physical theory, while strictly physicalist accounts risk excluding higher-level causation altogether. We argue that this dilemma stems from a conflation of physical determination with causation. To address this issue, we distinguish between two complementary descriptive frameworks: the physical stance and the causal stance. While the physical stance represents systems in terms of state evolution, the causal stance introduces asymmetric relations that enable the explicit representation of internal mechanisms. We show that causal descriptions provide a more constrained and informative representation of internal structure and cannot, in general, be reconstructed from physical descriptions alone. Within this framework, we define mental causation in terms of intrinsic causes and propose the Dual-Laws Model (DLM), which explicitly implements whole-to-parts causal mechanisms. This approach provides a principled way to model the causal role of consciousness without violating physical determinism.

Existing Causal-Why Video Question Answering (VideoQA) models often struggle with higher-order reasoning, relying on opaque, monolithic pipelines that entangle video understanding, causal inference, and answer generation. These black-box approaches offer limited interpretability and tend to depend on shallow heuristics. We propose a novel, modular paradigm that explicitly decouples causal reasoning from answer generation, introducing natural language causal chains as interpretable intermediate representations. Inspired by human cognitive models, these structured cause-effect sequences bridge low-level video content with high-level causal reasoning, enabling transparent and logically coherent inference. Our two-stage architecture comprises a Causal Chain Extractor (CCE) that generates causal chains from video-question pairs, and a Causal Chain-Driven Answerer (CCDA) that derives answers grounded in these chains. To address the lack of annotated reasoning traces, we introduce a scalable method for generating accurate causal chains from existing datasets. We construct human verified causal chains for 46K samples. We also propose CauCo, a new evaluation metric for causality-oriented captioning. Experiments on three large-scale benchmarks demonstrate that our approach not only outperforms state-of-the-art models, but also yields substantial gains in explainability, user trust, and generalization -- positioning the CCE as a reusable causal reasoning engine across diverse domains. Project page: https://paritoshparmar.github.io/chainreaction/

This paper develops a formal account of causal explanation, grounded in a theory of conversational pragmatics, and inspired by the interventionist idea that explanation is about asking and answering what-if-things-had-been-different questions. We illustrate the fruitfulness of the account, relative to previous accounts, by showing that widely recognised explanatory virtues emerge naturally, as do subtle empirical patterns concerning the impact of norms on causal judgments. This shows the value of a communication-first approach to explanation: getting clear on explanation's communicative dimension is an important prerequisite for philosophical work on explanation. The result is a simple but powerful framework for incorporating insights from the cognitive sciences into philosophical work on explanation, which will be useful for philosophers or cognitive scientists interested in explanation.

Existing algorithms for explaining the output of image classifiers use different definitions of explanations and a variety of techniques to find them. However, none of the existing tools use a principled approach based on formal definitions of cause and explanation. In this paper we present a novel black-box approach to computing explanations grounded in the theory of actual causality. We prove relevant theoretical results and present an algorithm for computing approximate explanations based on these definitions. We prove termination of our algorithm and discuss its complexity and the amount of approximation compared to the precise definition. We implemented the framework in a tool ReX and we present experimental results and a comparison with state-of-the-art tools. We demonstrate that ReX is the most efficient black-box tool and produces the smallest explanations, in addition to outperforming other black-box tools on standard quality measures.

Causal video question answering (QA) has garnered increasing interest, yet existing datasets often lack depth in causal reasoning. To address this gap, we capitalize on the unique properties of cartoons and construct CausalChaos!, a novel, challenging causal Why-QA dataset built upon the iconic "Tom and Jerry" cartoon series. Cartoons use the principles of animation that allow animators to create expressive, unambiguous causal relationships between events to form a coherent storyline. Utilizing these properties, along with thought-provoking questions and multi-level answers (answer and detailed causal explanation), our questions involve causal chains that interconnect multiple dynamic interactions between characters and visual scenes. These factors demand models to solve more challenging, yet well-defined causal relationships. We also introduce hard incorrect answer mining, including a causally confusing version that is even more challenging. While models perform well, there is much room for improvement, especially, on open-ended answers. We identify more advanced/explicit causal relationship modeling & joint modeling of vision and language as the immediate areas for future efforts to focus upon. Along with the other complementary datasets, our new challenging dataset will pave the way for these developments in the field. Project Page: https://github.com/LUNAProject22/CausalChaos