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.
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.
Explainable Artificial Intelligence aims to make black-box models more trustworthy by presenting, in a human-understandable manner, the elements that lead to the model's output. This involves both (i) identifying components and connections with genuine causal influence on outputs and (ii) translating such structures into an interpretable representation. For the former, we introduce CIExplainer, a novel perturbation-based method grounded in causal inference for explaining Graph Neural Networks (GNNs). CIExplainer identifies the subgraph with the highest causal effects on GNN predictions using the Potential Outcome Framework. We evaluate and compare CIExplainer on various GNN architectures (GCN, GraphSAGE, GAT, GIN) and datasets. To bridge subgraph explanations with human interpretability, we further propose G2TeXplainer, a method that transforms causal subgraphs into natural language explanations that capture both feature-level and relational information.
Francisco Caldas, Sahil Satish Kumar, Ruben Belo +1
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.