Graph Counterfactual Explanations

Graph neural networks (GNNs) predict molecular properties from chemical graph data, but predictive accuracy does not explain how graph information supports an individual decision. A compact prediction-preserving rationale does not necessarily reveal which changes reverse the decision or which modifications the model tolerates. We propose the Multi-Perspective Graph Explainer (MPGE), unifying factual support, counterfactual sensitivity, and exemplar tolerance for a frozen classifier. The factual view, originally termed prototype (PT), seeks a compact retained edge set with the same label and required confidence. Counterfactual (CF) explanations seek bounded prediction-changing deletions; exemplar (EXE) explanations seek non-trivial bounded deletions that preserve the label and confidence. A shared constrained formulation connects prediction behavior, compactness, and edit cost, while separate objectives generate the three views. Our graph-classification extension of CF-GNNExplainer learns symmetric edge rankings and verifies discrete candidates, recording unsuccessful searches. A separate BBBP fragment backend returns RDKit-sanitized molecules. We evaluate the primary GCN implementation on MUTAG, Mutagenicity, AIDS, COX2_MD, and BBBP using semantic coverage, conditional quality, stability, and runtime. Successful factual masks retained 8.6%--15.5% of input edges on average across datasets; bounded counterfactual coverage was 4.8%--67.6%, and exemplar preservation coverage was 98.9%--100.0%. Exploratory controls reveal the influence of hard projection and retained node information. Quantitative comparisons and molecular visualizations characterize model support, sensitivity, and tolerance without treating them as validated chemical mechanisms.

Counterfactual explanations of graph neural networks identify edge deletions that flip a prediction. On heterogeneous graphs, however, existing methods first collapse the graph into untyped edges, so they cannot answer the question a domain expert actually asks: which relation type drives this prediction? We present RACE (Relation-Aware Counterfactual Explanations), which gives this question an exact, per-instance answer. For every explained instance, an exhaustive search over relation subsets returns the certified minimum relation-deletion set that flips the prediction -- or an explicit report that no such deletion exists; each relation-level answer is then refined into a typed edge set within the attributed relations, verified on the discrete model by single-edge restoration. The relation-level answer is exact and deterministic given the frozen backbone, whereas soft-mask baselines vary by 6-8 pp in success rate across runs differing only in random ordering. On ACM, a Cora-derived graph, and ogbn-mag, RACE improves counterfactual success rate over the strongest baseline by up to +2.7 pp while deleting fewer edges, and attains the highest success rate among all same-task baselines on every dataset; the advantage reproduces across four backbones on ogbn-arXiv and on DBLP, with cross-seed relation-set agreement up to 0.89. A synthetic study with known generating mechanisms confirms that the search recovers the relation the trained model actually relies on -- and reports infeasibility rather than fabricating an attribution when the model has learned none -- so the explanations stay trustworthy exactly where explanations matter.

Can a trace explaining model execution also compute the changes needed for a specified alternative prediction? We propose trace-guided intervention search, which uses executable reasoning traces as an intermediate representation for intervention synthesis. A Specified-Foil Counterfactual edits past events so that a frozen temporal predictor selects a designated foil. Our method constructs facts and replacement values from completed original and foil executions and recovered unmet conditions. Proposal generation constructs edits and selects candidates within a fixed cap; exact replay verifies foil top-1 outcomes among retained edits and compositions. Implemented in LiFTER for continuous-time dynamic graphs (CTDGs) and TLogic for temporal knowledge graphs (TKGs), the method improves success over coordinate-based proposal generation by 13.7-34.7 percentage points on four CTDG datasets and 60.0-83.3 points on two TKG datasets under matched downstream search and a proposal cap of 32. Separate shared-candidate comparisons retain 85.7-93.6% of black-box greedy's CTDG success rate with 75.0-80.0% fewer predictor evaluations. A Pulse case study confirms simulator-level survival for five of six interventions. Executable traces thus provide both explanatory evidence and a reusable computational representation for constructing and testing specified alternatives.

Counterfactual explanations for graph-structured data seek to determine minimal and realistic modifications required in an input graph to alter a model's prediction to a predefined output. Although counterfactual explainers that support modifying the graph by both adding and removing edges have recently emerged, there is still a lack of general and efficient methods, especially when considering the quality of the generated explanations. Moreover, the problem remains far from solved, as existing methods exhibit different strengths and weaknesses, often trading off between explanation size, coverage and quality. For this reason, it is important to identify where each method performs well and where it falls short, so as to guide future research in the field. Thus, our study compares six state-of-the-art (SOTA) models on a diverse set of real-world and synthetic datasets, covering both binary and multi-class graph and node classification tasks, and evaluates their performance using diverse quantitative and qualitative metrics.

Real-world decision-making in public health and social science can greatly benefit from predictive models, yet translating predictions into effective interventions requires explaining the model behavior. While Graph Neural Networks (GNNs) are well-suited for modeling relational data, existing explanation methods largely operate at the node level and fall short of supporting actionable, network-level intervention design. Existing counterfactual GNN explainers, such as CF-GNNExplainer and CF$^2$, rely on continuous mask optimization over features and edges, which implicitly assume feasible edge manipulation, may allocate effort to immutable or non-actionable attributes, and incur substantial computational overhead. Further, the method of arriving at the explanation itself is difficult to explain to a domain specialist who is not an AI expert. Can simple methods generate good explanations? To explore this, we reframe counterfactual explanation as an intervention design problem. At the local level, we generate counterfactuals via a greedy search that directly identifies minimal, actionable changes to node features and neighbor-level conditions. We derive conditions under which the greedy search provides guarantees, and empirically show that these conditions are approximately met. These counterfactuals are converted into interpretable rules suitable for real-world intervention. At the network level, we formulate intervention selection as a Disjunctive Normal Form (DNF) coverage problem under a budget constraint, which is nondecreasing and approximately submodular, enabling a greedy algorithm with theoretical guarantees. Experiments on synthetic graphs and real-world suicide risk networks demonstrate that our approach produces scalable, cost-effective intervention strategies with significantly improved efficiency over mask-based counterfactual methods.

Graph Neural Networks (GNNs) achieve strong predictive performance on graph-structured data across domains such as chemistry, biology, and network analysis, yet they provide no intrinsic explanation of their predictions. This limits their adoption in high-stakes and safety-critical settings. Counterfactual explanations address this by revealing the minimal structural modifications that would change a model's prediction. On graphs, however, such a modification is hard to produce. The search space is discrete and combinatorial, and a valid answer must respect categorical node and edge types together with domain rules such as chemical valency in the case of molecular graphs. Existing explainers give up one of two things. Either edits are not held on the data manifold, or the search does not span the full edit space. We propose Graph Diffusion Counterfactual Explanation via Inversion (GDCE-I), which gives up neither. A discrete denoising diffusion model with a novel discrete inversion scheme enables distribution-aware edits leveraging the whole domain edit space. We further address the incomplete and inconsistent evaluation of graph counterfactuals by deriving a framework of explanation desiderata and applying it to every method under one shared protocol. Across four benchmarks, GDCE-I outperforms related work by a large margin on the defined framework. For the molecular domain, we further qualitatively show that GDCE-I attains interpretable in-distribution solutions.

Oscillatory signals, such as vibration, carry class-discriminative information in specific frequency bands; perturbing them in raw feature space for counterfactual analysis easily destroys their temporal structure and produces physically implausible results. In this work, we introduce IMFACT (IMF-based counterfACTuals), a model-agnostic framework for generating plausible counterfactual explanations for time series classifiers that operates in the decomposition space of Empirical Mode Decomposition. An input signal is split into Intrinsic Mode Functions (IMFs), and selected IMFs are progressively substituted with those of a Nearest Unlike Neighbour (NUN) until the classifier flips to the target class. We evaluate six IMF-selection strategies and a multi-NUN cycling extension on two UCR benchmarks (FaultDetectionA, FruitFlies). The variance-based strategy with three NUNs outperforms two prominent baseline techniques on reliability and plausibility metrics, while cycling across three NUNs yields the best proximity across both datasets.

Predictive maintenance relies on accurate Remaining Useful Life estimation, often formulated using survival analysis over multivariate time-series data. While modern deep survival models achieve strong predictive performance, their black-box nature limits their use in safety-critical settings where actionable insight is required. In this work, we introduce SurvCF(t), the first framework for generating counterfactual explanations for survival models operating on time-series data. SurvCF(t) identifies minimal, plausible, and temporally consistent changes to an asset's operational history that increase its predicted life time, framing explanation as a constrained optimization problem combining validity, proximity, sparsity, and plausibility. We evaluate the method on multiple benchmarks, including C-MAPSS, N-CMAPSS, and a real-world case study of the Scania Component_X dataset, demonstrating its ability to produce actionable and interpretable interventions. Our results show that SurvCF(t) bridges the gap between survival prediction and prescriptive maintenance, enabling explainable and decision-oriented AI for maintenance strategies.

Counterfactual explanations (CEs) for multivariate time-series classifiers are often difficult to interpret in domains where experts reason in terms of semantic feature groups rather than individual channels. In rehabilitation movement analysis with multi-sensor inertial measurement units (IMUs), clinicians interpret motion through muscle-group and joint-segment abstractions; yet, most existing counterfactual methods operate at the channel level, producing scattered and biomechanically incoherent explanations. We propose a two-stage framework for group-based counterfactual generation in high-dimensional IMU data. We first show that Shapley-Adaptive (SA) group ranking preserves counterfactual validity but fails to enforce group-level sparsity, motivating the need for explicit group selection. We then introduce Learnable Gate (LG) methods, which incorporate trainable per-group relevance gates jointly optimized with perturbation masks. Experiments on the KneE-PAD rehabilitation dataset demonstrate that LG substantially improves modality-group sparsity compared to the channel-level M-CELS baseline while maintaining or improving validity, temporal smoothness, and generation efficiency. Exercise-specific analyses further show that group-structured counterfactuals yield concise, muscle-level corrective guidance aligned with clinical reasoning. Overall, the proposed framework enhances interpretability without sacrificing counterfactual quality, enabling more actionable explanations for rehabilitation movement analysis.

Decision-making with deep learning-based time series forecasting requires not only accurate predictions but also actionable insights. However, current architectures do not inherently provide such information. Specifically, guidance is needed on how current conditions must be modified to shift from a predicted outcome to a desired future scenario. Counterfactual explanations provide a natural framework for this task, as they represent minimal input changes that alter the model's prediction, indicating when and how intervention is required. Existing approaches rely on instance-wise optimization, leading to inconsistency across instances, high computational costs, and limited applicability in real-time settings. To address these limitations, we reformulate counterfactual generation for time series forecasting as the problem of learning a globally consistent intervention strategy, allowing counterfactuals to be generated through a single shared function. We propose Counterfactual Time Series Explanations (ConTex), a model-agnostic, decomposed architecture comprising a temporal context encoder and a conditional encoder, followed by two heads that capture interventions in terms of temporal relevance and modification strength. This structure overcomes the instability and inconsistency of instance-based approaches by producing targeted, interpretable interventions across time and feature dimensions in a single forward pass, making it suitable for real-time applications. Across multiple forecasting architectures and benchmark datasets, ConTex achieves state-of-the-art validity while generating sparse counterfactuals that minimize the number of necessary interventions. Additionally, our approach reduces computational cost by at least 12-36x compared to instance-wise generation and supports real-time inference at approximately 0.007 seconds.

Node representation learning, such as Graph Neural Networks (GNNs), has emerged as a pivotal method in machine learning. The demand for reliable explanation generation surges, yet unsupervised models remain underexplored. To bridge this gap, we introduce a method for generating counterfactual (CF) explanations in unsupervised node representation learning. We identify the most important subgraphs that cause a significant change in the k-nearest neighbors of a node of interest in the learned embedding space upon perturbation. The k-nearest neighbor-based CF explanation method provides simple, yet pivotal, information for understanding unsupervised downstream tasks, such as top-k link prediction and clustering. Consequently, we introduce UNR-Explainer for generating expressive CF explanations for Unsupervised Node Representation learning methods based on a Monte Carlo Tree Search (MCTS). The proposed method demonstrates superior performance on diverse datasets for unsupervised GraphSAGE and DGI.

As AI models grow more complex, explainability is essential for building trust, yet concept-based counterfactual methods still face a trade-off between expressivity and efficiency. Representing underlying concepts as atomic sets is fast but misses relational context, whereas full graph representations are more faithful but require solving the NP-hard Graph Edit Distance (GED) problem. We propose U-CECE, a unified, model-agnostic multi-resolution framework for conceptual counterfactual explanations that adapts to data regime and compute budget. U-CECE spans three levels of expressivity: atomic concepts for broad explanations, relational sets-of-sets for simple interactions, and structural graphs for full semantic structure. At the structural level, both a precision-οriented transductive mode based on supervised Graph Neural Networks (GNNs) and a scalable inductive mode based on unsupervised graph autoencoders (GAEs) are supported. Experiments on the structurally divergent CUB and Visual Genome datasets characterize the efficiency-expressivity trade-off across levels, while human surveys and LVLM-based evaluation show that, on CUB, the retrieved structural counterfactuals are frequently judged semantically equivalent to, and often preferred over, reference deterministic GED-based explanations.

Counterfactual explanations emerge as a powerful approach in explainable AI, providing what-if scenarios that reveal how minimal changes to an input time series can alter the model's prediction. This work presents a survey of recent algorithms for counterfactual explanations for time series classification. We review state-of-the-art methods, spanning instance-based nearest-neighbor techniques, pattern-driven algorithms, gradient-based optimization, and generative models. For each, we discuss the underlying methodology, the models and classifiers they target, and the datasets on which they are evaluated. We highlight unique challenges in generating counterfactuals for temporal data, such as maintaining temporal coherence, plausibility, and actionable interpretability, which distinguish the temporal from tabular or image domains. We analyze the strengths and limitations of existing approaches and compare their effectiveness along key dimensions (validity, proximity, sparsity, plausibility, etc.). In addition, we implemented an open-source implementation library, Counterfactual Explanations for Time Series (CFTS), as a reference framework that includes many algorithms and evaluation metrics. We discuss this library's contributions in standardizing evaluation and enabling practical adoption of explainable time series techniques. Finally, based on the literature and identified gaps, we propose future research directions, including improved user-centered design, integration of domain knowledge, and counterfactuals for time series forecasting.

We present a new method for generating plausible counterfactual explanations for time series classification problems. The approach performs gradient-based optimization directly in the input space. To enforce plausibility, we integrate soft-DTW (dynamic time warping) alignment with $k$-nearest neighbors from the target class, which effectively encourages the generated counterfactuals to adopt a realistic temporal structure. The overall optimization objective is a multi-faceted loss function that balances key counterfactual properties. It incorporates losses for validity, sparsity, and proximity, alongside the novel soft-DTW-based plausibility component. We conduct an evaluation of our method against several strong reference approaches, measuring the key properties of the generated counterfactuals across multiple dimensions. The results demonstrate that our method achieves competitive performance in validity while significantly outperforming existing approaches in distributional alignment with the target class, indicating superior temporal realism. Furthermore, a qualitative analysis highlights the critical limitations of existing methods in preserving realistic temporal structure. This work shows that the proposed method consistently generates counterfactual explanations for time series classifiers that are not only valid but also highly plausible and consistent with temporal patterns.