A Computationally Feasible Framework for Causal Probabilistic Explanation

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.

Witnesses Explain Anomalies

Unsupervised anomaly detection scores each point of an unlabelled, contaminated sample in a single pass, and increasingly must also explain why a point is flagged. Yet the dominant detectors give a score with no account of which features drive it, and explanations are bolted on post-hoc with SHAP or LIME, which re-query the detector thousands of times per point and only approximate it. We introduce WAND, an unsupervised tabular anomaly detector that is explainable by design. WAND organises its computation around directions on the unit sphere, scoring each point by how far its projection escapes a sub-Gaussian extreme-value baseline. The originality of our approach is that the witness directions that flag a point, being vectors in feature space, are its explanation, a per-feature attribution obtained at no cost over scoring and, since the score is differentiable, recoverable by gradients. Scoring is linear in the sample size, and a probe-efficiency bound guarantees every anomaly a witness, hence an explanation. Across 47 ADBench datasets WAND attains the best mean Friedman rank at ROC-AUC parity with 16 unsupervised baselines, so the gain is interpretability at no accuracy cost; its native explanations are more accurate and faithful than post-hoc SHAP/LIME and ECOD at a fraction of the query cost. WAND is thus a practical, interpretable solution for explainable anomaly detection.

Assessing Alignment and Stability of Feature Importance Explanations via Weight of Evidence

Feature importance Methods (FIMs) are widely used in Explainable AI to interpret model predictions, yet attribution scores alone often provide limited insight into the underlying reasoning process. In this work, we introduce a novel perspective by embedding FIMs within a hypothesis-testing framework based on Weight of Evidence (WoE). We quantify how strongly the observed evidence supports any given hypothesis on feature importance. The reference hypothesis can stem from domain knowledge, ground truth, or be derived from the FIM itself. This formulation enables a principled evaluation of FIMs, capturing both their alignment with prior knowledge and their variability. We further provide theoretical results linking WoE to attribution variance. Empirical results shows the applicability and flexibility of our strategy analyzing LIME and SHAP explanations in settings with different reference hypotheses. Overall, our framework offers a complementary tool for assessing FIMs through a contrastive, evidence-based lens.

Actionable CBFI: Integrating Structural Decomposition and Causal Counterfactual Recourse for Tabular Machine Learning

Explainable artificial intelligence (XAI) increasingly calls for actionable counterfactual recourse, yet current methodologies face challenges related to causal invalidity, excessive cognitive burden, and predictive failure. Exhaustive causal search algorithms often require modifications to multiple attributes, whereas additive attribution-guided methods, such as SHAP, ignore higher-order feature synergies, leading to suboptimal predictive momentum and diffuse intervention effort in complex nonlinear models, such as XGBoost. To bridge this gap, we introduce actionable case-based feature importance (A-CBFI), a diagnosis-prescription integrated framework for tabular machine learning. Grounded in structural causal models (SCMs), A-CBFI isolates synergistic interaction bottlenecks and releases suppressive structural locks, translating them into targeted interventions. By mathematically separating the active user intervention space (L_{\mathrm{active}}) from downstream effects and concentrating over 98.3% of the intervention effort on diagnosed root causes, A-CBFI enables highly targeted interventions. Empirical evaluations across the financial and healthcare domains demonstrate that A-CBFI reduces the active human intervention burden by 76.9% while maintaining comparable global recourse cost to exhaustive causal baselines. By prioritizing the diagnosed causal bottlenecks, A-CBFI provides targeted and actionable recourse while maintaining causal validity and achieving full relative convergence across all causally feasible instances.

Towards A Unified Information Bottleneck Framework for Time Series Explanations

Explaining deep learning models operating on time series data is crucial in various applications that require transparent and interpretable insights into model behavior. {Existing explanation methods generally fall into two categories: attribution-based explanations, which identify the temporal regions most responsible for a prediction, and counterfactual explanations, which reveal how an input should be modified to alter the model's decision.} {Despite valuable insights, these two fields are largely studied independently. This disconnect leaves attribution methods lacking causal validation, while counterfactual methods suffer from severe instability, producing adversarial-like noise instead of meaningful explanations.} In this work, we revisit time-series explainability from an information-theoretic perspective and show that existing explainers are vulnerable to trivial solutions and distributional shifts. To address these limitations, we propose a unified objective function for explainable time series learning that bridges attribution and counterfactual reasoning within a single framework. Building upon the Information Bottleneck principle, our formulation explicitly prevents trivial explanations and out-of-distribution counterfactuals. {Based on this objective function, we introduce {\modelname}, a novel explanation framework that learns a parametric transformation network to construct explanation-embedded instances, where preserved information yields attribution explanations and controlled information removal produces stable counterfactual explanations.} We evaluate {\modelname} on synthetic and real-world benchmarks against state-of-the-art baselines. Extensive quantitative and qualitative results show that {\modelname} consistently outperforms competing methods, yielding faithful attributions and stable counterfactual explanations.

NVExplain: Explaining Time Series Forecasting with Latent Trajectory Analysis and Structure-Preserving Surrogates

Time series forecasting models are widely used in high-stakes settings, yet their predictions remain difficult to interpret because existing post-hoc methods often ignore temporal dependence and fail to provide horizon-specific explanations. We propose a model-agnostic explainability framework that explains forecasting predictions by attributing each forecast horizon to temporally relevant historical lags. The framework models forecasting as a latent trajectory and introduces semantic flow to quantify how information evolves across time in the model's internal representations. By aggregating semantic flow, it constructs a lag-horizon attribution matrix that captures horizon-resolved temporal influence. To improve explainability, we further generate structure-preserving perturbations and fit sparse local surrogate models, producing human-readable and temporally coherent explanations. We evaluate the method using faithfulness and stability diagnostics across multiple benchmark datasets. Results show that the semantic-flow variant achieves competitive or superior faithfulness compared to standard post-hoc baselines, while being substantially more computationally efficient. Stability analysis further demonstrates that the explanations are robust and identifies regimes where interpretation should be applied with caution.

Leaf Values as Coordinates: Exact Contrastive Explanation for Gradient-Boosted Ensembles

A gradient-boosted ensemble predicts by summing one leaf value per tree. Read those values as coordinates rather than as intermediate results, and every instance becomes a point in R^M on which the model acts linearly: the score is the sum of the coordinates. This small change of view makes contrastive explanation exact. The difference between two instances is a vector that is identically zero wherever they share a leaf, so the gap between a rejected applicant and an accepted one is carried by a handful of coordinates, each traceable to a real split in a real tree. Nothing is fitted, sampled, or assumed additive in features -- the additivity is already there, in the right space. We build a recourse method on this representation and evaluate it on five tabular datasets under repeated cross-validation. Its recommendation reconstructs the model's own decision to 6.2 x 10^-15, so an auditor can re-check the arithmetic without the model. On the credit datasets it is Pareto-non-dominated on effort against realism. And when recommendations are restricted to changes the subject could actually make -- not their age, not a settled delinquency -- it retains 58% of its validity where the strongest baseline retains 41%, a distinction the standard evaluation cannot see because it never asks whether a recommendation can be carried out.

CAS: A Causal Attribution Score for Local and Global Explainable Artificial Intelligence

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.

JAPE: Joint Anomaly Prediction and Intrinsic Explanation in Multivariate Time Series

Multivariate time-series anomaly prediction aims to identify whether and when anomalies will occur over a future horizon from historical observations. Existing methods primarily characterize anomalies as deviations in future numerical values, which may overlook subtle dependency changes induced by weak anomaly precursors and provide no native variable-level explanation together with the alert. To bridge these gaps, we propose JAPE, a Joint Anomaly Prediction and Explanation framework that lifts anomaly prediction from numerical-deviation modeling to dependency-structure modeling. JAPE is the first anomaly prediction framework to explicitly model evolving dependency structures for both point-wise alerting and native variable-level explanation. Specifically, JAPE (i) proposes a Decoupled Spatio-Temporal Representation (DSTR) backbone that decouples temporal and spatial modeling and captures lag-aware dependencies via learnable lag aggregation, thereby perceiving structural precursors before numerical deviations emerge; (ii) designs a dual-view alerting mechanism that fuses numerical forecasts with evolving dependency graphs for point-wise anomaly prediction, capturing structural evidence even under subtle numerical deviations; and (iii) presents Native Predictive Explanation (NPE), which directly reuses the predicted dependency graphs to rank variables by structural deviations without additional models or training. Extensive experiments on five real-world benchmarks across three prediction horizons demonstrate that JAPE improves average F1 and AUC-PR by 19.7% and 41.3%, respectively, while improving explainability with 26.6% gain in MRR.

RelShap: Relationally Consistent Shapley Explanations

Machine learning pipelines commonly flatten relational data into single-table representations, discarding structural constraints. Widely used Shapley value-based feature attributions then rely on feature independence, evaluating the model on combinations that could never arise in the underlying data, producing misleading explanations. We propose RelShap, a framework that incorporates relational constraints and data provenance into Shapley value computation, restricting both background data and coalition evaluation to relationally valid configurations. The framework is estimator-agnostic and composes with Kernel SHAP, Monte Carlo, and Leverage SHAP without altering their sampling or weighting properties. Functional dependencies further induce equivalence classes over feature coalitions, which RelShap exploits to reduce runtime without changing Shapley values; we provide a combinatorial characterization of the expected speedup. Experiments across multiple datasets, models, and estimators show that RelShap produces explanations that are more faithful to the data-generating process, correctly identifying the dominant feature in controlled settings where existing methods, including Conditional SHAP and ManifoldShap, do not. Our code is available at: https://github.com/duneag2/relshap.

BREAD: Baseline-Referenced Explanations for Anomaly Diagnosis

Artificial Intelligence (AI)-based prospective anomaly detection methods are increasingly deployed in high-dimensional and nonlinear settings. Among these approaches, AI-based statistical process monitoring (SPM) is widely used, providing a structured framework for prospective monitoring. Once an anomaly is detected, a diagnosis method is needed to identify the features driving the flagged observation away from normal behaviour. Traditional SPM diagnosis methods are typically designed for specific detection models and cannot be directly applied to AI-based methods. Model-agnostic explainable AI (XAI) offers a general framework for feature relevance explanation. However, existing methods suffer from scalability limitations or assign relevance to noise features, reducing diagnosis accuracy. We propose a scalable, baseline-referenced diagnosis method that uses both the anomalous observation and normal baseline information. We provide mathematical guarantees that under a mean-shift anomaly setting, the proposed method achieves higher faithfulness in detecting the features causing the anomaly compared to LIME. Simulation studies and a real-world case study validate the effectiveness of the proposed method and show that it generates more faithful and accurate diagnosis results for AI-based prospective anomaly detection methods.

Backward Compatibility in Tree-Based Explanations and Enhanced CART Algorithm

In the operation of machine learning models, model update is a fundamental process that requires careful consideration of its impact on downstream decision-making. Particularly when operating explainable models, changes in explanations resulting from model updates can lead to detrimental outcomes for users. Decision trees, due to their high transparency, are frequently employed in risk-sensitive decision-making and serve as a prominent example in which the aforementioned issue is evident. However, existing research addressing similar issues has focused on explanations based on feature contributions, and thus cannot handle explanations derived from tree structures. Therefore, this paper proposes the Backward Compatibility Loss in Tree-based eXplanations (BCLTX), a loss metric that suppresses changes in decision tree explanations before and after updates. Furthermore, we design CART with Backward Compatibility in Tree-based eXplanations (CART-BCTX), a lightweight algorithm that improves upon CART for the decision tree update problem under BCLTX. Experimental results using 10 real-world datasets, including both classification and regression tasks, show that CART-BCTX achieves favorable trade-offs between prediction performances and BCLTX values, with comparable computation times to CART, regardless of the task.

Beyond Feature Importance: A Comparative Analysis of Pattern Detection Methods in Cluster Interpretation

Interpreting clustering outcomes remains a fundamental challenge in data analysis, particularly in domains such as healthcare where meaningful patterns must be extracted from high-dimensional data. While numerous explainability techniques exist, they are primarily designed to assess feature importance or provide local instance-level explanations rather than to identify structured patterns present within clusters. This work presents a comparative evaluation of commonly used post-hoc analysis methods for pattern detection in clustering results. To enable controlled evaluation, we introduce a suite of synthetic datasets in which predefined patterns are systematically injected. Three widely used techniques are evaluated: a Random Forest surrogate model with permutation feature importance, LIME (Local Interpretable Model-agnostic Explanations), and principal component analysis. Results demonstrate that although each method can successfully recover relevant features, none consistently detects all injected pattern types. These findings high- light a critical gap between existing explainability tools and the requirements of pattern-level cluster interpretation, motivating the development of dedicated pattern detection methodologies.

GENESIS: Towards Explainable Causal Discovery

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.

Information Bottleneck Learning for Faithful Time Series Forecasting Explanations

As forecasts increasingly drive decisions in fields such as energy, transportation, and healthcare, understanding the historical data behind these predictions has become as crucial as the predictions themselves. Although existing interpretable-by-design forecasters reveal their internal structures, they offer no guarantee that these structures faithfully reflect the underlying evidence driving the predictions. In contrast, while faithfulness-oriented methods explicitly verify model behavior, they are almost exclusively designed for post-hoc classification tasks. To bridge this gap, we propose IB-Forecast, an inherently interpretable multivariate time-series forecasting framework. It decomposes forecasting into a learned periodic component and a residual component computed with explainable masks over input tokens. With a budget-constrained information bottleneck, end-to-end optimization enables users to directly control explanation sparsity. With a rigorous faithfulness evaluation protocol, extensive experiments demonstrate that IB-Forecast matches the forecasting error of leading black-box models while providing faithful explanations at no additional inference cost. Furthermore, under a matched sparsity budget, these native explanations consistently surpass gradient-based, occlusion-based, and optimization-based baselines across all evaluated datasets. Ultimately, whereas the native explanations of existing interpretable forecasters exhibit poor faithfulness, IB-Forecast guarantees high explanation fidelity, requiring only 14-20% of the observations to deliver low-error predictions.

FADEx: Feature Attribution and Distortion-based Explanation of Dimensionality Reduction

Dimensionality Reduction (DR) is a fundamental tool for high-dimensional data exploration, reducing the complexity of latent spaces of machine learning models, and assisting in the explanation of complex opaque models. However, non-linear DR techniques often function as opaque transformations themselves, making it challenging to understand how individual features influence instance positioning in the reduced space. This lack of transparency complicates the analysis and interpretation of structural patterns, hindering the ability to reason about the organization of high-dimensional data based on the projected layout. In order to address this challenge, dimensionality reduction explanation methods have shown promise in improving the understanding of the observed groups and cluster structures. Unfortunately, existing DR explanation approaches tend to suffer from limitations such as multiple attributions per feature and restricted applicability to specific dimensionality reduction methods, which hinder their use. In this work, we propose FADEx, a novel local per-instance feature attribution method that leverages local linear approximation via first-order Taylor expansion and Singular Value Decomposition to provide explanations. FADEx computes the local linear models via weighted least squares, eliminating the need for out-of-sample data mapping, making it agnostic to the DR method, while simultaneously providing local feature attributions and distortion analysis. Through qualitative and quantitative evaluations, comparisons with existing methods, and case studies, we demonstrate FADEx's effectiveness and versatility in providing explanations and analytical resources for analyzing the behavior of DR methods. The results indicate FADEx yields robust and reliable explanations, outperforming existing approaches in several aspects.

Variable Importance Identification Through Lazy Training for Binary Classification

Deep neural networks have been widely used in many applications (e.g., computer vision and natural language processing); however, understanding their explainability remains a challenging task. Recently, substantial research has been devoted to improving the explainability of deep neural networks, with most of this work focusing on the regression framework. In this paper, we instead focus on the binary classification framework and adopt a variable-importance framework combined with the idea of lazy training to propose an efficient algorithm for identifying important features. From a theoretical perspective, our method relies on only a minimal set of assumptions and achieves well-controlled error rates. The validity of the proposed method and algorithm is examined through extensive simulation studies and real-data applications.

Beyond Sufficiency: Time Series Explanation with Counterfactual Necessity

Faithful explanations of time-series classifiers should identify subsequences that are not only sufficient to preserve a black-box model's prediction, but also necessary for maintaining it. However, existing sufficiency-oriented methods can assign high importance to spurious subsequences that support the prediction without being essential to the model's decision. We introduce \textbf{TimePNS}, a necessity-aware framework for time-series explanation. Inspired by Pearl's counterfactual notion of necessity, TimePNS assesses whether a temporal factor is necessary by intervening on it and measuring whether the original prediction is disrupted. The framework adopts a two-stage design. Stage I learns an identifiable causal generative process together with a sufficiency-oriented explanation mask. Stage II performs counterfactual interventions on temporal factors to derive necessity signals, which supervise a temporal gate that refines the initial explanation by suppressing non-essential components and emphasizing counterfactually necessary ones. Experiments on synthetic and real-world time-series benchmarks show that TimePNS more accurately identifies decision-critical subsequences and consistently improves sufficiency-necessity trade-offs over strong baselines.

User-Centric Modeling of Transactional Sequences with Explainable State Space Models

We propose a hybrid approach for user-centric modeling of transactional event sequences that combines contrastive representation learning (CoLES) with State Space Models (SSMs). While contrastive methods yield high-quality compressed user representations, existing encoders -- RNNs and Transformers -- suffer from vanishing gradients or quadratic complexity, respectively. Mamba, a selective SSM, efficiently handles long-range dependencies but remains underexplored for personalized user analysis. We investigate two integration strategies: (1)~initializing the Mamba hidden state with a CoLES embedding, and (2)~prepending the projected CoLES embedding as a prefix token to the input sequence. Both approaches supply the model with an informative user prior from the first step. Experiments on three public datasets -- Age (multiclass age-group prediction), MBD (multi-label product acquisition), and Taobao (binary purchase prediction) -- demonstrate consistent improvements over standalone Mamba and CoLES with a linear classifier, with the hybrid models converging 2--3$\times$ faster than the plain SSM baseline. Explainability analysis via discretization-step maps and Integrated Gradients reveals selective event filtering on behavior-rich datasets and identifies the most informative transaction features.

Feature Attribution-Based Explainability Analysis of Deep Learning Models in Predictive Process Monitoring

Predictive process monitoring supports the optimization and control of operational business processes by forecasting the future state or outcome of ongoing cases. While deep neural networks have achieved strong performance for these tasks by modeling sequential dependencies in event logs, their black-box nature limits trust and practical adoption. Feature attribution methods are often used to address this, but applying them directly poses a dilemma: event-level attributions impose high computational complexity for long traces, while explanations based on aggregated trace representations often fail to capture the underlying control-flow dynamics. To address this issue, we propose a local post-hoc explainability method for deep neural networks in outcome prediction. The method relies on a control-flow-aware segmentation algorithm that partitions a trace into meaningful segments and supports the computation of segment-level SHAP explanations. This makes it possible to identify which parts of a trace influence a prediction and which change points steer the case toward the predicted outcome. We assess the proposed segmentation method on a synthetic dataset with known process logic, where meaningful change points can be explicitly verified, and we demonstrate its usefulness on real-world event logs from a loan application process and an administrative process of a Dutch municipality.

Challenges of Explainability in Continual Learning for Time Series Forecasting

Deep learning models have shown strong potential for time series forecasting, yet their deployment in real-world environmental monitoring remains challenging due to non-stationary dynamics and limited explainability. In this work, we investigate explainability as a central tool for understanding continual learning in adaptive time series forecasting, with Experience Replay strategies. We study neural forecasting architectures such as PatchMixer, PatchTST and DLinear, augmented with attention-based sampling mechanisms to support model adaptation over time. Explainability is leveraged through attention rollout and gradient-based attribution methods (Grad-CAM) to analyze both predictive behavior and sampling strategies within a continual learning framework. Experiments conducted on real-world piezometric time series exhibiting heterogeneous patterns and regime shifts show that analyzing model and sampling behaviors provides valuable insights into the dynamics of the continual learning framework. Beyond predictive performance, our results highlight the challenges and opportunities of using explainability to understand continual learning behaviors, revealing how attribution patterns evolve over time and how they can inform data selection and adaptation strategies in non-stationary forecasting scenarios.

Decision-Value Attribution in Predict-then-Optimize Systems

Predictive models are increasingly embedded in operational decision-making, yet standard explanation methods typically explain forecasts rather than the decisions those forecasts induce. This distinction is important in predict-then-optimize systems: large forecast changes may leave the optimizer's action unchanged, while small changes can alter the selected decision and its realized value. We propose Decision Value Attribution (DVA), a Shapley-based framework for attributing the value of a fixed prediction--optimization pipeline. The framework defines cooperative games whose payoff is the downstream decision value, allowing the players to be information sources, optimization or design parameters, or both. We present three variants: InfoDVA attributes value to features, DesignDVA attributes value to operational configurations, and Decision-Value Interactions (DVI) quantifies how information and design jointly create value. We further distinguish post-DVA, which evaluates decisions using realized outcomes, from pre-DVA, which evaluates decisions under the model's full prediction. This separation turns attribution into a decision-level diagnostic of whether the model's operational beliefs align with realized performance. The resulting attributions are expressed in the units of the operational objective and decompose the gain or loss relative to a baseline. Case studies in electricity storage arbitrage and emergency medical service coverage show that predictive explanations can be poor proxies for operational value, that DVA can guide targeted information-control interventions, and that optimization configurations determine when predictive information is decision-relevant.

The Failures of Marginal Influence-Based Attribution Methods for Global Time Series Explanations

Explainability methods for time series models predominantly produce flat attribution scores: they quantify the direct influence of a feature at a timestamp by a scalar. We prove that the dominant failure mode of such methods is not the scalar format itself but a fundamental computational mismatch: existing methods compute scores via marginal conditioning or off-manifold gradients, both of which conflate direct temporal dependencies with mediated ones under autocorrelation. We also define DAG-faithfulness: an explanation is DAG-faithful if the temporal dependency graph it encodes is Markov-equivalent to the temporal directed acyclic graph (DAG) implicitly learned by the model. Particularly, we observe that standard attribution methods, specifically SHAP, are not DAG-faithful in general, and that recent time-series-aware extensions inherit the same computational limitation.

Explainable Outlier Detection for Interval-valued Data

Explainability is increasingly recognized as a key aspect of outlier detection. However, for complex data structures such as interval-valued data, it remains largely unexplored. Building on an outlier detection framework based on the Interval Minimum Covariance Determinant estimator, we propose a novel approach to explain the outlyingness of interval-valued observations using the concept of the Shapley value. We derive a closed-form expression for the Shapley value of the squared robust Interval-Mahalanobis distance, enabling efficient computation of variable contributions. This formulation allows for a fine-grained interpretation of outliers, providing a detailed decomposition into contributions from centers, ranges, and cross-terms of the interval-valued observations. Moreover, the Shapley value is closely connected to the concept of cellwise outliers, as it can help identify variable-specific outliers that may not be evident at multivariate level. We further extend the framework through the Shapley interaction index to capture pairwise variable interactions driving atypical behavior. The practical utility of the proposed approach is illustrated through two real-world datasets.

Beyond Shapley: Efficient Computation of Asymmetric Shapley Values

We address the problem of explainability in machine learning models through feature attribution methods. In particular, we consider a variant of Shapley values known as Asymmetric Shapley Values (ASV), which enables the incorporation of causal knowledge into model-agnostic explanations through the use of a causal graph. We show that in certain contexts in which the computation of SHAP is $\#P$-hard, the exact computation of ASV can be done in polynomial time. To extend this algorithmic result, we introduce a notion of equivalence classes over the topological orderings of the underlying causal graph, which is useful to reduce the time to compute ASV. In particular, we present a polynomial-time algorithm (in the number of equivalence classes) to compute it whenever the causal graph is a rooted directed tree. Finally, we develop an algorithm for approximating ASV in arbitrary causal DAGs which relies on a procedure to sample topological orderings uniformly at random. To implement this sampling mechanism we leverage known algorithms as well as simpler alternatives. Our experimental results demonstrate the practical viability of the proposed approach in realistic causal structures.

The Representational Limit of Scalar Interactions: An Interventional Decomposition

Signed pairwise interaction scores fundamentally conflate uniqueness (U), redundancy (R), and synergy (S). We prove this on a minimal 3-way XOR structural causal model: faithful indices such as Shapley-Taylor return zero per pair, whereas projective indices such as Shapley Interaction spread the third-order effect into pair scalars that conflate the three mechanisms. We introduce Stochastic Hi-Fi, a post-hoc, retraining-free predictability decomposition that estimates per-feature U/R/S profiles by interventional masked inference. The estimator provides exact interventional semantics, finite-sample Monte Carlo bounds, strict variance reduction from coupled diamond sampling, and uniform finite-vocabulary convergence. Across tabular SCMs, Stochastic Hi-Fi recovers structure missed by scalar baselines (up to 411x larger interaction-magnitude recovery ratios). It also separates redundant and synergistic heads in the GPT-2 IOI circuit. On NIH ChestX-ray14, Stochastic Hi-Fi matches GradCAM on Pointing Game and improves substantially on Deletion AUC.

P$^2$CE: Model-Agnostic Plausible Pareto-Optimal Counterfactual Explanations

The increasing use of machine learning algorithms in social applications has raised concerns about fairness and transparency, leading to the development of counterfactual explanations. These explanations supports individuals to understand and potentially alter unfavorable decisions in areas such as loan applications, job selections, and more, by providing actionable changes to input features that would lead to a desired outcome. Existing methods often struggle to balance feasibility, plausibility, and computational efficiency. To address this, we introduce P$^2$CE, an algorithm for generating plausible Pareto-optimal counterfactual explanations, offering users a diverse set of optimal trade-offs between different notions of feasibility. P$^2$CE employs an auxiliary isolation forest outlier detector to ensure that explanations are in accordance with the data distribution and leverages SHAP values to obtain optimal results with short computing times, regardless of the underlying model. Our algorithm was empirically evaluated on three datasets, demonstrating superior performance in terms of both solution quality and computational efficiency compared to related techniques.

E4GEN: Event-level Explainable Extreme-Enhanced Time-series Generation

Generating realistic time series is essential for scientific research and real-world applications. However, existing methods often emphasize overall distributional fidelity while failing to faithfully capture extreme events. To advance existing research, we propose E4GEN, an explainable diffusion framework for extreme event-aware time-series generation. E4GEN provides systematic insights into when, what, and how to control extreme-event generation through three key components. First, E-Activator learns the dataset-adaptive extreme-control signal activation step during the denoising process without interfering with regular temporal components, including trend and seasonality. Second, E-Predictor determines what control signal to enforce through Self-Driven Semantic Prediction, where each sample derives its own control signal by inferring latent extreme-event information during generation. It also includes a novel Data-Conditioned Training, Noise-Initiated Sampling mechanism to address the issue of unavailable training labels. Third, E-Control specifies how to control extreme-event generation through a trainable Extreme Control Network, which transforms the semantic control signal into layer-wise signals and injects it into the denoising process. We evaluate E4GEN on six datasets with 17 metrics, and extensive experiments show that E4GEN outperforms state-of-the-art models across multiple dimensions, including overall fidelity, extreme-event fidelity, and downstream utility.

Manifold-Aligned Guided Integrated Gradients for Reliable Feature Attribution

Feature attribution is central to diagnosing and trusting deep neural networks, and Integrated Gradients (IG) is widely used due to its axiomatic properties. However, IG can yield unreliable explanations when the integration path between a baseline and the input passes through regions with noisy gradients. While Guided Integrated Gradients reduces this sensitivity by adaptively updating low-gradient-magnitude features, input-space guidance still produces intermediate inputs that deviate from the data manifold. To address this limitation, we propose \emph{Manifold-Aligned Guided Integrated Gradients} (MA-GIG), which constructs attribution paths in the latent space of a pre-trained variational autoencoder. By decoding intermediate latent states, MA-GIG biases the path toward the learned generative manifold and reduces exposure to implausible input-space regions. Through qualitative and quantitative evaluations, we demonstrate that MA-GIG produces faithful explanations by aggregating gradients on path features proximal to the input. Consequently, our method reduces off-manifold noise and outperforms prior path-based attribution methods across multiple datasets and classifiers. Our code is available at https://github.com/leekwoon/ma-gig/.