Shapley Value Attribution

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3 papers in the last four weeks, against 2 the four weeks before. 0.0% of all new papers.

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Latest papers 69

Oct 8, 2026cs.LG

Interval-valued SHAP in Tree-Based Models

Shapley values are among the most popular feature-attribution explanations. Efficient approaches for computing/estimating Shapley values for tree-based models, which are state-of-the-art for tabular data sets, have been developed. However, it is known that Shapley values can be (highly) unrobust due to small and realistic changes. In this paper, we propose an imprecise Dirichlet model (IDM) based method to analyze the robustness of Shapley values in decision trees and random forests. Technically, it is done by quantifying and analyzing the interval-valued Shapley values when a few unannotated instances are randomly introduced to the leaves of the trees. The interval-valued Shapley values can be defined following common principles in handling incomplete data: the pessimistic and averaging principles. We derive various theoretical results that lead to efficient computation of the interval-valued Shapley values. We also show that the proposed method can be straightforwardly generalized to the case of Banzhaf values. We then present various case studies and experiments to illustrate the behaviour of the proposed interval-valued Shapley values and their applications in debiasing uninformative features.

Chenrui Zhu, Vu-Linh Nguyen, Marie-Hélène Masson +1

Université de technologie de Compiègne, UMR-CNRS 7253 Heudiasyc Compiègne, France · IUT de l’Oise, Université de Picardie Jules Verne Beauvais, France

Shapley Value Attribution Feature Attribution Random Forest

Oct 7, 2026stat.ML

From Log-Odds to Shapley Values: An Explanatory Geometry for the Weighted Naive Bayes Classifier

This paper studies the construction of an explanatory space for a weighted naive Bayes classifier from the supervised representation induced by the model. We start from the classical supervised distance based on conditional log-likelihoods and introduce a discriminative reformulation based on log-odds, which is more directly related to the classification decision. We then show that this representation induces a distance that exactly coincides with the

\ell_1

distance between vectors of analytical Shapley values, thereby providing a formal explanatory interpretation of the geometry induced by the model. Finally, we empirically compare several supervised distances derived from these representations using a

k

-nearest neighbors classifier. This work highlights a close link between supervised distance, local explanation, and predictive behavior, from a primarily methodological perspective.

Vincent Lemaire, Fabrice Clérot

Orange Research, France

Classification Shapley Value Attribution

Sep 28, 2026stat.ML

A Hierarchy of Entropy-Shapley Games for Multivariate Predictive Uncertainty

Modern probabilistic machine learning models increasingly produce multivariate outputs with complex dependence structure, from multi-step time-series forecasts to sample path predictions. Understanding which input features drive the predictive uncertainty is important for risk-aware decisions, model diagnostics, and deciding whether the uncertainty should be mitigated or hedged against. This attribution problem requires a choice of how dependencies between output components are treated. Existing approaches reduce the output to a scalar through aggregation or projection before attribution, thereby obscuring whether features affect marginal uncertainty, dependence structure, or both, while component-wise analyses can miss dependence effects entirely. We close this gap by introducing a hierarchy of three entropy-based Shapley games that make this output-side choice explicit for any ordered multivariate outcome, ranging from per-component marginal entropy to fully joint entropy. The hierarchy isolates a cross-component attribution term that captures how each feature shifts the dependence between output components, a quantity invisible to component-wise methods. We establish a chain-rule decomposition of the joint attribution and characterize the cross-component term through conditional total correlation, providing both closed-form and sample-based estimators. Finally, we demonstrate how the framework captures differences in learned joint structure across probabilistic models from distributional regression to a zero-shot time series foundation model.

Niklas Koenen, Claudia Battistin, Jeriek Van den Abeele +1

Leibniz Institute for Prevention Research and Epidemiology – BIPS University of Bremen, Germany · Simula Research Laboratory Oslo, Norway · Telenor Research & Innovation Fornebu, Norway +1

Probabilistic Forecasting Shapley Value Attribution Uncertainty Decomposition

Sep 22, 2026cs.AI

CausalLoss-Fin: Attributing Financial-Agent Loss to Decisions and Infrastructure Faults

When an agent handling a payment exception loses money, the agent-step attribution methods this paper compares against will name one of its actions. They will do so even when a settlement message was dropped and the agent never had a chance: they intervene on agent actions and do not expose infrastructure faults as intervenable variables, so every dollar they explain is charged to a decision. We take a benchmark whose fault process is explicit and replayable, decompose each episode's realised delivery schedule into named, individually repairable messages, and intervene on both the agent's choices and the infrastructure's. A telescoping identity splits any policy's loss exactly three ways: an infrastructure effect, a policy differential against the best implementable policy, and a reference-policy residual. Two of the three can be negative, so none is a share; Shapley then divides the first into signed allocations over individual messages. One result is structural and needs no corpus: an agent-only baseline identifies no infrastructure cause, because its model contains no variable that could name one. What 545 planted episodes across 3 policies measure is the size of that consequence. It misfiles 100% of infrastructure episodes and charges $114,383.40 to the agent. Repairing what it names recovers 0.0% of the available loss; repairing a minimal sufficient set recovers 100.0%. Scoring messages one at a time is not merely imprecise: 27.8% (95% CI: 23.3--32.3%) of episodes do not decompose additively. We evaluate deterministic programmatic policies rather than language-model agents, which is what makes replay exact and which limits external validity to stochastic agents. The prevalence figures are properties of this generator, not field rates.

Abhishek Sharma

Agent Failure Analysis Financial Services Causal Attribution Shapley Value Attribution Fine-Grained Credit Assignment

Sep 14, 2026stat.ML

Shapley Value Estimation for Multi-Site Data with Blockwise-Missing Features

Shapley value (SV)-based methods are the prevailing framework for feature attribution in machine learning, yet existing population-level Shapley estimators generally assume that observations used to evaluate the coalitional game are fully observed under a common feature space. This assumption is routinely violated in multi-site studies across biomedicine, social science, and environmental monitoring, where institutions record different features under different protocols, producing systematic blockwise missingness across sources. We first show that the standard remedy of imputing missing features before computing Shapley values introduces systematic, coalition-dependent bias into the resulting attributions. We then propose \textbf{FUSHAP} (\textbf{Fu}sion \textbf{Sh}apley \textbf{A}ttribution from \textbf{P}artially-observed data), a method that leverages partially-observed auxiliary sites to reduce the variance of a preliminary single-site Shapley estimate without imputation. A permutation-based screening step detects and excludes sites whose data distributions are incompatible with the target population. In synthetic experiments, FUSHAP achieves

3

--

8\times

lower MSE than the single-site estimator and

2

--

3\times

lower MSE than imputation baselines without incurring imputation-induced bias, and the screening procedure identifies misaligned sites with

82\%

power at moderate misalignment and

100\%

for strong misalignment. On multi-site air quality and multi-center clinical data, FUSHAP reduces MSE by approximately

3

--

7\times

relative to the single-site estimator; in the clinical application, standard imputation can increase MSE above the single-site baseline.

Siqi Li, Wangxuan Fan, Yiming Li +2

Centre for Biomedical Data Science, Duke-NUS Medical School · School of Data Science, Chinese University of Hong Kong, Shenzhen · Department of Biostatistics, Columbia University +3

Feature Attribution Learning with Missing Data Shapley Value Attribution

Aug 13, 2026cs.AI

SkillShapley: Boundary-Adaptive Shapley Valuation for Skill Step Attribution in LLM Agents

Agent skills are crucial external instructions that enable language agents to execute long procedural tasks such as coding or document processing. Existing agent skills are primarily created through human manual crafting or agent execution traces, with limited understanding of how each step contributes to overall skill performance on specific tasks; i.e., there remains an open problem in quantifying the contribution of individual steps within an agent skill. To address this issue, we first model skill-step attribution as a Shapley value-based contribution estimation problem, and then propose SkillShapley, a step-level attribution framework for agent skills. Notably, SkillShapley operates in two phases, motivated by key empirical insights, i.e., discretized benchmark rewards that create sharp performance cliffs, and step interactions that are largely additive rather than synergistic. Specifically, it first identifies informative coalitional regions, and then adaptively samples new coalitions that can yield reusable marginal evidence. Experiments on skills from the widely adopted SkillsBench demonstrate that our SkillShapley can effectively and efficiently identify high- or low-value skill steps, providing several key takeaways for agent skill creation.

Chang Liu, Yuqi Zhang, Yiman Zhong +3

1Beihang University, Beijing, China · 2Shandong University, Jinan, China

LLM Agent Skill Learning Shapley Value Attribution

Aug 11, 2026cs.LG

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.

Seungeun Lee, Joao Fonseca, Julia Stoyanovich

New York University, New York, USA · INESC-ID, Lisbon, Portugal

Feature Attribution Shapley Value Attribution

Aug 5, 2026cs.AI

What Is a Skill Worth? Structure-Aware Shapley Valuation of Agent Skills

Agent skills are increasingly optimized by automated feedback loops, producing long structured artifacts whose internal value remains unclear. We study skill valuation: assigning credit to the internal units of a fixed skill, such as rules, examples, scripts, and heuristics, under a fixed agent and held-out task distribution. Skill valuation differs from data or prompt-span valuation because skill units are structured: they may depend on other units, belong to a document hierarchy, trigger agent behavior, and consume limited prompt context. We introduce SkillSV, a structure-aware Shapley-style framework for skill valuation. SkillSV compiles a skill into units, dependencies, and hierarchy, so that only valid counterfactual skills are evaluated. It uses paired deletion and length-neutral padding to separate content value from context cost, and estimates the resulting values with a rollout-budgeted estimator for noisy agent evaluations. On four agentic benchmarks, we assess the faithfulness, actionability, and explanation of SkillSV: it recovers unit interactions, preserves aggregate skill lift, and guides safe pruning and compression.

Tao Li, Junfeng Liu, Qinghua Zhao +5

1Nanjing University of Aeronautics and Astronautics · 2Pengcheng Laboratory · 3Hefei University +1

Agent Evaluation Shapley Value Attribution

Jul 31, 2026cs.LG

Shapley-Value-Based Feature Attribution for Data Masking

Despite its many benefits, widespread access to individuals' personal data also causes severe privacy concerns for consumers, companies, and policymakers. This study proposes a novel framework that adapts the Shapley-value-based feature attribution approach to the problem domain of data privacy by capturing the two crucial dimensions of data privacy---disclosure risk and data utility. Our proposed framework takes a holistic view of data masking through a fair feature attribution approach based on Shapley values. Different from the existing literature that mostly focuses on the risk-utility tradeoff at the dataset level, the proposed framework addresses the tradeoff at the feature level. Furthermore, the proposed framework is agnostic to data masking methods, statistical and machine learning methods, and data utility and disclosure risk evaluation metrics. Experimental results show that our proposed method can effectively reduce disclosure risk while preserving data utility.

Xinxue, Qu, Francis Bilson Darku +1

Shawn · Department of Information Technology, Analytics, and Operations, Mendoza College of Business University of Notre Dame, South Bend, IN, U.S.A. · Department of Information Systems, W. P. Carey School of Business Arizona State University, Tempe, AZ, U.S.A.

Shapley Value Attribution Privacy-Utility Tradeoff

Jul 25, 2026cs.CV

Explaining BiomedCLIP with Weighted Banzhaf Interactions Supported by Tree-Gram Parsing

Vision-Language Models (VLMs) are demonstrating significant capabilities in medical tasks like radiology analysis, yet providing faithful and interpretable explanations remains a key consideration for their responsible deployment in clinical settings. However, existing explanation methods, such as the widely used FIxLIP framework, often struggle with the fine-grained nature of modern tokenizers. The tokenization problem fragments clinical concepts---splitting terms like "saddle embolus" into scattered, meaningless subwords---which leads to noisy, semantically incoherent cross-modal attributions. Such fragmentation also results in a combinatorial explosion of interaction possibilities, obscuring the model's true reasoning. To address this, we introduce ParseFIxLIP, an extension that incorporates the Tree-Gram Parsing into the Banzhaf interaction game used by FIxLIP. This semantically informed strategy utilizes dependency parsing trees to define explanation players by grouping related text tokens into semantically coherent units. Our smart_depth grouping strategy, merging tokens according to spaCy token dependency tree, successfully mitigates concept fragmentation, yielding substantially more interpretable cross-modal interactions by unifying complex medical concepts. Quantitatively, while baselines struggled with the high dimensionality of long captions, our parsing approach maintained statistical robustness and semantic parsimony. Qualitative analysis on BiomedCLIP, validated on medical imagery (ROCOv2) and general examples, confirms that the approach accurately captures the synergistic influence of grouped words on model predictions. In conclusion, our work offers intuitive and clinically relevant insights into VLM decision-making, fulfilling the critical need for coherent explanations in the medical domain.

Jakub Rymarski, Adam Rempała, Bartłomiej Sobieski +1

University of Warsaw, Poland · Centre for Credible AI, Warsaw University of Technology, Poland

VLM Interpretability Shapley Value Attribution Medical VLMs

Jul 23, 2026cs.LG

A Polynomial Architecture-Attribution Co-Design Framework for Exact Aumann-Shapley Attribution in GNNs

We study feature-level and node-level explanations for graph neural networks (GNNs) through the lens of Aumann-Shapley attribution. Path-integral methods such as Integrated Gradients provide an axiomatic formulation of attribution, but their practical use in deep GNNs typically relies on finite-sample numerical approximations to the path integral, requiring a trade-off between quadrature error and computational cost. This paper proposes APEX, a model-attribution co-design framework that makes the attribution integral exactly computable under a polynomial GNN architecture. The key component is PolyGIN, a GIN-style graph network whose message-passing, normalization, and transformation operations preserve a bounded multivariate polynomial form for scalar model scores, such as pre-softmax logits. We show that, for a PolyGIN with

L

polynomial transformation blocks, the derivative along the attribution path has degree at most

2^L-1

. Therefore, Gauss--Legendre quadrature can evaluate the Aumann--Shapley path integral exactly, up to floating-point precision, with

2^{L-1}

deterministic evaluation points. The resulting attributions can be computed at the feature level and then aggregated into node-level scores while preserving completeness. Experiments on synthetic and real-world graph benchmarks show that PolyGIN maintains competitive predictive performance, while the complete APEX framework achieves higher attribution fidelity than the compared baselines and substantially reduces the number of evaluations required for path integration.

Bizu Feng, Zhimu Yang, Shuming Wang +4

Institute of Artificial Intelligence Innovation and Industry, Fudan University, Shanghai, China · Shanghai Academy of AI for Science, Shanghai, China · Human Phenome Institute, Fudan University, Shanghai, China +1

Gradient-Based Attribution Polynomial Neural Networks Graph Neural Networks Shapley Value Attribution GNN Explainability

Jul 21, 2026cs.AI

Fishing Out Free Riders: Shapley-Based Reward Attribution for Parallel Reasoning via Reinforcement Learning

Large Language Models (LLMs) excel at multi-step reasoning, yet current parallel reasoning approaches often fail to distinguish the contributions of individual reasoning paths. Many paths may be redundant, misleading, or even detrimental, but outcome-level rewards assign uniform reward, leading to ambiguous learning signals and unstable training. We propose Parallel Shapley, a reinforcement learning framework that attributes fine-grained, path-level contributions in multi-path reasoning. Treating each path as a player in a cooperative game, we leverage Shapley values to quantify marginal contributions, using a generative reward model to evaluate path utilities and Monte Carlo sampling for efficient approximation. Experiments on mathematical reasoning benchmarks show that Parallel Shapley outperforms existing baselines while providing more stable and interpretable training. Our framework effectively "fishes out the free riders," assigning reward proportionally and improving multi-path reasoning in LLMs.

Wentao Zhang, Haoyu Zhang, Xinke Jiang +7

ShanghaiTech University · City University of Hong Kong · Peking University +2

RL for Language Model Reasoning Shapley Value Attribution Large Reasoning Models

Jul 19, 2026cs.CR

How Jailbreak Attacks Inform Safety Alignment: A Defender-Centric, Shapley-Based Evaluation of Jailbreak Contributions

Jailbreak attacks on large language models are usually evaluated by attacker-centric metrics such as attack success rate (ASR), yet an attack that breaks a model is not necessarily useful for improving its safety. We propose a defender-centric view of jailbreak evaluation, where attacks are evaluated by the downstream safety improvements they enable when used as red-teaming data for safety training. Building on this view, we introduce A-MESS (Minimal Effective Attack-Subset Selection), a setting-agnostic framework for attributing and selecting jailbreak attacks from black-box subset utility observations. A-MESS estimates AttackSHAP, a Shapley-based score that attributes marginal utility to individual attacks and selects compact attack subsets under user-specified budgets via greedy or surrogate-based optimization. Across controlled utility landscapes and real LLM safety settings, we find that ASR rankings are weakly aligned with defender-centric utility, that AttackSHAP can be estimated accurately with limited utility queries, and that directly optimizing subsets yields stronger safety utility than attacker-centric or attribution-only selection. These results suggest evaluating jailbreak attacks as resources for improving safety, not only as tools for breaking models.

Yukai Zhou, Feiyang Lu, Xiaokai Mao +2

ShanghaiTech University · Zhejiang University

LLM Safety Alignment Training Data Selection Shapley Value Attribution LLM Jailbreak Attacks LLM Safety Evaluation

Jul 18, 2026cs.LG

Counterfactual Shapley Credit Assignment

The Credit Assignment Problem (CAP) is fundamental to developing efficient and explainable Reinforcement Learning (RL) agents. Existing frameworks, whether relying on temporal contiguity or hindsight-conditioned reward reweighting, frequently fail to attribute properly between an agent's policy (skill) and environmental stochasticity (luck). A principled approach to CAP must isolate the true causal drivers of observed outcomes from spurious correlations and environmental randomness. We introduce Counterfactual Shapley Credit Assignment, a novel framework grounded in causal theory that attributes credit and blame via the Counterfactual Shapley Value (

φ

-value). By redistributing environmental rewards,

φ

-values enhance temporal credit assignment across three critical dimensions: sparse causality, high stochasticity, and delayed rewards, all while preserving the optimal policy. We derive a consistent estimator that computes

φ

-values efficiently, enabling a new class of policy gradient methods,

φ

-PPO, combined with Prioritized Trajectory Replay (PTR). Empirical results demonstrate that

φ

-values align precisely to the ground truth causes of task rewards with superior sample efficiency in challenging environments where prior state-of-the-art methods fail to converge.

Mingxuan Li, Kai-Zhan Lee, Elias Bareinboim

Department of Computer Science, Columbia University, New York, NY, USA

Credit Assignment in RL Temporal Credit Assignment Shapley Value Attribution Sparse-Reward RL Counterfactual Credit Assignment Counterfactual Learning

Jul 15, 2026cs.LG

Local Additive Feature Attribution: A Mathematical Taxonomy and Reporting Checklist

Feature-attribution methods are central to explainable artificial intelligence. Their assumptions are expressed in several mathematical languages: cooperative-game values, path integrals, gradient operators, perturbation distributions, and backpropagation rules. This survey proposes a common framework for local additive feature attribution. It organizes Shapley, path-based, gradient/backpropagation, perturbation, and CAM-style methods around five specification choices: value function, reference, path, perturbation distribution, and conservation rule. It then compares these methods through an axiom-by-method matrix and links common failure modes, including baseline sensitivity, off-manifold perturbations, sanity-check failures, adversarial manipulation, and method disagreement, to the assumptions that produce them. Finally, the survey proposes a ten-item reporting checklist for studies that use local additive attributions. The central message is that attribution results are meaningful only relative to the mathematical assumptions under which they are defined, and that those assumptions should be reported.

Rebecca Afriyie Sarpong, Daniel Commey

Gradient-Based Attribution Feature Attribution Perturbation-Based Feature Attribution Shapley Value Attribution Explainability Evaluation

Jul 12, 2026cs.LG

Exact and Certified Data Shapley for Weighted k-Nearest-Neighbor Regression and Soft-Label Prediction

Data Shapley is the standard principled answer to which training points are worth what, and its k-nearest-neighbor (KNN) specialization is the version deployed in practice: the exact estimator shipped by toolkits such as pyDVL and OpenDataVal. Exact algorithms are known for unweighted KNN and for weighted KNN classification, but weighted KNN regression and soft-label prediction have resisted: the only exact method is an O(N^K) brute force, exponential in neighborhood size K. The obstruction: the weighted regression prediction is a ratio of two coalition-dependent sums, whose normalization denominator breaks the additive, threshold, and duplication structures the prior polynomial algorithms rely on. We close this gap. We give (i) the first pseudo-polynomial-time exact algorithm (polynomial in N and K at fixed lattice precision) for weighted KNN-regression Data Shapley, a counting dynamic program over the joint integer state (sum of w, sum of w*y), verified against exhaustive enumeration with zero mismatch on 12,716 adversarial instances; (ii) a certified FPTAS for continuous weights and targets, with a machine-checkable per-value error certificate never violated across 86,400 checks; (iii) a complexity landscape, including an unconditional Omega(D_w) output-size lower bound and access-model hardness results; and (iv) a weighted soft-label multi-class extension. We release an open-source, CPU-only library and the first exact weighted-regression Data Shapley ground truth. On downstream mislabel detection our exact values are statistically equivalent to Monte-Carlo Data Shapley (dataset-level TOST, n=8, p<10^-4), the pre-registered outcome; the value of exactness is instead determinism, a certified error bound, and an exact reference for auditing estimators: Monte-Carlo did not reproduce the exact top-10% ranking at any budget tested, up to 3,000 permutations (~1.28e6 utility evaluations).

Zongye Lyu

Faculty of Information Technology, Monash University, Melbourne, VIC 3800, Australia

Shapley Value Attribution k-Nearest Neighbors Approximation Algorithms

Jul 10, 2026cs.LG

Nonlinear Axiomatic Attribution for Cooperative Games

The Shapley value is a widely used concept in attribution problems, as it uniquely satisfies the axioms of linearity, consistency, equal treatment, and efficiency. Often, the inclusion AUC metric is used to evaluate the quality of player rankings, in order to identify positively participating players. However, it can be established that the Shapley value is not always reliable for this purpose. The core issue lies in its linearity: the Shapley value acts as a linear operator with an excessively large null space, which is likely to contain non-negligible perturbations that remain indistinguishable to the operator. To address this limitation, we explore the design of nonlinear axiomatic attribution methods. Inspired by the least core, which is a popular nonlinear substitute for the Shapley value, we introduce a class of nonlinear attribution methods that retain the remaining necessary axioms. Each method yields a contribution vector that is the unique optimal solution to a minimization problem, which aims to approximate utility functions as faithfully as possible. In terms of the inclusion AUC metric, our experiments demonstrate the potential effectiveness of these methods compared to Shapley value variants that relax only the efficiency axiom. Our code is available at https://github.com/watml/nonlinear-axiom.

Weida Li, Zhuanghua Liu, Yaoliang Yu +1

Department of Computer Science, National University of Singapore, Republic of Singapore · School of Computer Science, University of Waterloo, Canada · Vector Institute, Canada

Cooperative Game Theory Feature Attribution Shapley Value Attribution

Jul 4, 2026cs.LG

Validation-Induced Shapley Shifts: How Validation Structure Distorts Data Valuation

Shapley values are widely used to attribute value to training data based on their marginal contribution to performance on a validation set. Existing practice often assumes these values are stable once the training data and model are fixed. In this work, we uncover a systematic vulnerability: even modest changes to the validation set, such as introducing noises, cause directional shifts in Shapley distributions. As noises are added, Shapley values of training samples compress toward zero. We trace this to a noise-induced neighborhood reshuffling effect: perturbations alter the local rank order between validation and training samples, flattening the valuation landscape. Using the KNN-Shapley framework, we show through synthetic and real data that these shifts are consistent and reproducible. Our findings challenge the assumption of Shapley stability and reveal a new axis of fragility in data valuation. We propose normalization and boundary-aware validation strategies to mitigate these distortions and enable more robust, interpretable valuation in machine learning marketplaces.

Yinan Shen, Ziao Yang, Hongfu Liu

Adobe Waltham, MA 02451, USA · Department of Computer Science Brandeis University Waltham, MA 02453-2728, USA

Shapley Value Attribution Data Valuation Training Data Attribution

Jul 2, 2026stat.ML

Autorelevance function and other feature relevance measures for univariate time series

We propose a model agnostic methodology to measure lag relevance in machine learning forecasting models applied to univariate time series. Particularly, we are working in the context of time series using the frameworks of Ghost variables and Shapley values, together with additive importance measures, to introduce the auto-relevance and partial auto-relevance functions as the lag importance values. Additionally, we propose a novel method to replace absent features in coalition based methods with a one step forecast from the same model. We evaluate these proposals under different simulations and real data cases. This combined framework perspective is particularly suitable for time series. In addition, to show our discoveries we use a pull of models from the seasonal ARMA family and recurrent neural networks. We found that the calculated relevance measures successfully demonstrate the expected lag structure in almost all cases.

Julian Cardenas, Jamie Arjona, Pedro Delicado

Departament d’Estad´ıstica i Investigaci´o Operativa, Universitat Polit`ecnica de Catalunya - BarcelonaTech, C/ Jordi Girona 1-3, Barcelona, 08034, Catalunya, Spain.

Explainable Time Series Forecasting Feature Attribution Time Series Forecasting Shapley Value Attribution

Jul 1, 2026q-fin.CP

Shapley in Context: Explaining Financial Language with Domain Expertise

In recent years, large language models have achieved remarkable success and have seen growing adoption in financial applications. At the same time, explainability remains critical in finance, a domain characterized by high stakes and strict regulatory requirements. Although numerous methods have been proposed to explain black box machine learning models, the majority of these approaches are designed for general purpose tasks and do not incorporate domain specific knowledge. In this work, we study the explainability of financial textual data modeled by large language models through the lens of the Shapley value. Specifically, we investigate whether Shapley based attributions align with established financial domain knowledge. Through rigorous theoretical analysis and extensive empirical evaluations, we demonstrate that Shapley values can yield explanations that are consistent with financial reasoning and can offer meaningful insights into the model's behavior in text based financial applications.

Dangxing Chen, Pengzhan Guo

Zu Chongzhi Center, Duke Kunshan University, Kunshan, Jiangsu, CN · Digital Innovation Research Center, Duke Kunshan University, Kunshan, Jiangsu, CN

LLM Interpretability Shapley Value Attribution Explainability Evaluation

Jun 29, 2026cs.LG

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.

Konstantinos Ziliaskopoulos, Alexander Vinel, Alice E. Smith

Auburn University, Industrial & Systems Engineering, 36849, Auburn, AL, USA · University of Alabama, Mechanical Engineering & Computer Science, 35487, Tuscaloosa, AL, USA

Feature Attribution Predict-Then-Optimize Shapley Value Attribution

Jun 27, 2026cs.GT

Exit-and-Join Dynamics and Equilibrium in Continuum Cooperative Games

This paper develops a continuum theory of exit-and-join coalition dynamics in nonatomic cooperative games. We extend the Aumann-Shapley value and the Aumann-Drèze value to coalition structures in which each coalition is treated as a restricted nonatomic game, yielding a marginal-contribution-based payoff density that governs incentives for agents to remain in, exit, or join coalitions. We derive deterministic mean-field dynamics from decentralized switching rules and show that payoff-difference switching recovers replicator dynamics as a special case. We characterize exit-and-join equilibrium by the absence of profitable positive-mass deviations and prove its equivalence with stationarity of the induced mass dynamics under incentive-compatible and strictly payoff-responsive switching rates. For mass-based cooperative games, we construct a Lyapunov function and establish global convergence under strict concavity. We further show that the equilibrium is equivalent to a Wardrop equilibrium of an induced nonatomic population game and admits a variational inequality formulation. The framework is extended to incorporate switching costs and endogenous coalition acceptance rules, leading to constrained equilibria characterized by quasi-variational inequalities. The proposed theory unifies cooperative value allocation, noncooperative coalition mobility, mean-field dynamics, evolutionary game theory, and population games within a common framework for analyzing coalition formation and adaptation in large-scale multi-agent systems.

Quanyan Zhu

Department of Electrical and Computer Engineering · New York University Tandon School of Engineering · Brooklyn, NY, USA

Cooperative Game Theory Shapley Value Attribution

Jun 26, 2026cs.LG

OperatorSHAP: Fast and Accurate Shapley Value Estimation for Neural Operators

Understanding model predictions is essential for physical applications, where outputs often inform safety-critical decisions, such as structural load assessment, weather warnings, and clinical diagnosis. Shapley values satisfy many desirable properties as an attribution method, but their computational cost during inference hinders their practical use. Current amortized explainers, such as FastSHAP, are limited to homogeneous inputs, which is problematic for physical applications where data often comes from irregular grids and geometries. We introduce OperatorSHAP, a grid-agnostic attribution method and training procedure that allows us to train FastSHAP-like explainers for neural operators. We establish a theoretical framework for attributions in function space, connecting to Aumann-Shapley values. We further show that OperatorSHAP's explanations are consistent with state-of-the-art discrete Shapley values across resolutions and transfer across grid sizes without retraining.

Joshua Stiller, Santo M. A. R. Thies, Felix Czaja +1

LMU Munich, MCML · LMU Munich · LMU Munich, MCML, DFKI

Shapley Value Attribution Neural Operators

Jun 23, 2026cs.AI

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.

Ezequiel Companeetz, Santiago Cifuentes, Sergio Abriola

Departamento de Computación, Facultad de Ciencias Exactas y Naturales, UBA · Instituto de Ciencias de la Computación (ICC), CONICET

Cooperative Game Theory Feature Attribution Causal Attribution Shapley Value Attribution Causal Interpretability

Jun 22, 2026cs.LG

Do Location Encoders Capture Spatial Effects? A GeoShapley Benchmark Across Scales

Location encoders transform geographic coordinates into high dimensional embeddings for downstream machine learning, but it is unclear how well these representations capture interpretable spatial effects. We benchmark whether GeoShapley, a game-theoretic explainer that treats all location features as a single joint player, can recover spatially varying coefficients from models built on location-encoder embeddings. Eleven encoders from the TorchSpatial framework are evaluated against a synthetic process with known coefficients, across three scales (grid, county, global), with and without raw coordinates alongside the embedding, and under untrained and contrastively trained conditions. Measuring recovery as the correlation between estimated and true coefficients, we report how it varies with scale and encoder architecture and compare the embeddings against a raw-coordinate baseline. Recovery of the primary coefficient is consistently high across encoders, whereas recovery of a secondary coefficient is more scale-dependent, differing most at the global scale; the raw-coordinate baseline remains competitive throughout.

Daniel Kiv, Shaowen Wang

Siebel School of Computing & Data Science, University of Illinois Urbana-Champaign Urbana, IL, USA · Department of Geography & GIS and Siebel School of Computing & Data Science, University of Illinois Urbana-Champaign Urbana, IL, USA

Geospatial Representation Learning Shapley Value Attribution

Jun 17, 2026stat.ML

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.

Potito Aghilar, Sabino Roccotelli, Stanislao Fidanza +3

Polytechnic University of Bari · University of Bari Aldo Moro

Feature Interaction Modeling Representation Disentanglement Shapley Value Attribution Causal Interpretability

Jun 13, 2026cs.AI

Feature Attribution in Directed Acyclic Graphs Using Edge Intervention

Shapley value-based feature attribution methods face challenges in scenarios involving complex feature interactions and causal relationships, even when a causal structure is provided. Existing methods typically adopt a node-centric view, attributing importance solely to individual features. Consequently, they often fail to simultaneously capture the externality and exogenous influence of features, leading to unreasonable interpretations. To overcome these limitations, we propose a novel feature attribution method called DAG-SHAP, which is based on edge intervention. DAG-SHAP treats each feature edge as an individual attribution object, ensuring that both externality and exogenous contributions of features are appropriately captured. Additionally, we introduce an approximation method for efficiently computing DAG-SHAP. Extensive experiments on both real and synthetic datasets validate the effectiveness of DAG-SHAP. Our code is available at https://github.com/ZJU-DIVER/DAG-SHAP.

Qiheng Sun, Junxu Liu, Xiaokai Mao +4

The Hong Kong Polytechnic University, Hong Kong, China · Zhejiang University, Hangzhou, China · University of Illinois Urbana-Champaign, Urbana, USA

Feature Attribution Shapley Value Attribution Causal Interpretability

Jun 11, 2026cs.CR

MAStrike: Shapley-Guided Collusive Red-Teaming on Multi-Agent Systems

Hierarchical multi-agent systems (MAS) are rapidly being deployed in high-stakes workflows across domains such as finance and software engineering. In these systems, safety and security are inherently distributed across role-specialized agents, significantly expanding the attack surface, particularly under coordinated adversarial behaviors such as privilege escalation and cross-agent collusion. Existing red-teaming approaches for MAS remain limited: they rely on heuristic selection of target agents and perturb isolated message streams, leaving critical questions unanswered as which agents are most responsible for system safety, and how compromised agents can coordinate to bypass defenses. We propose MAStrike, a closed-loop framework for collusive red-teaming in hierarchical MAS. We propose the first agent-level Shapley value analysis for MAS, quantifying each agent's marginal contribution to system robustness under task-specific distributions. GGuided by this attribution, MAStrike identifies vulnerable agent coalitions and generates coordinated, role-aware adversarial manipulations. These attacks are iteratively refined through structured causal diagnosis, attributing failure cases to uncompromised agents that block adversarial attempts. We further build a comprehensive MAS red-teaming benchmark and controllable environments spanning diverse hierarchical topologies and domains, including finance, software engineering, and CRM. Extensive experiments across MAS built on multiple frontier models show that MAStrike substantially outperforms heuristic baselines. Our analysis further uncovers non-trivial Shapley value distributions and higher-order interaction structures among agents, revealing critical vulnerabilities and coordination patterns that are overlooked by prior single-agent or template-based methods.

Chejian Xu, Zhaorun Chen, Jingyang Zhang +5

University of Illinois, Urbana-Champaign · Virtue AI · University of Chicago +3

AI Agent Security Benchmarks Shapley Value Attribution Multi-Agent Systems Automated Red Teaming Multi-Agent System Security

Jun 1, 2026stat.ML

ShaplEIG: Bayesian Experimental Design for Shapley Value Estimation

Shapley values are a principled attribution measure widely used in interpretable machine learning, but their exact computation scales exponentially with the number of players, motivating a wide range of approximation methods based on value function evaluations of sampled coalitions. This raises the question of whether approximation accuracy can be improved by adaptively selecting coalitions for evaluation based on previous evaluations. This is particularly relevant in settings where the value function is costly and the number of evaluations is severely limited, such as retraining-based feature importance, data valuation, and hyperparameter importance. For this purpose, we propose ShaplEIG, a Bayesian experimental design approach that approximates the expensive value function using a Gaussian process surrogate and adaptively selects coalitions based on their expected information gain about the Shapley values. By the linearity of the Shapley values in the value function, we show that the expected information gain is available in closed form. Furthermore, we propose an efficient computation scheme that reduces the complexity from exponential to polynomial in the number of players via elementary symmetric polynomials. In extensive experiments across diverse costly applications, our method consistently improves sample efficiency in the low-budget regime over state-of-the-art baselines.

David Rundel, Fabian Fumagalli, Maximilian Muschalik +2

Department of Statistics, LMU Munich, Munich, Germany · Munich Center for Machine Learning, Munich, Germany · Institute for Informatics, LMU Munich, Munich, Germany +2

Shapley Value Attribution Adaptive Sampling Bayesian Experimental Design

Jun 1, 2026cs.GT

A Framework for Graph-Conditioned Hierarchical Shapley Attribution in Patent Valuation

Estimating the economic contribution of a single patent inside a product that embodies tens of thousands of patents is a long-standing unsolved problem in intellectual property economics. We propose PatentXAI, a framework that treats patent valuation as a problem of explainable AI: given a characteristic function v(S) encoding the revenue achievable by patent subset S, a patent's Shapley value measures its fair share of product profit in a way that satisfies efficiency, symmetry, dummy, and additivity. To make computation tractable we restrict each patent's coalition to its Markov Blanket inside a knowledge graph, grounded in the C-SVE conditional independence theorem (Li et al., 2020). Scaling experiments from n=12 to n=100 patents using Pareto-distributed coverage graphs report median Markov Blanket size of 32.9 percent of n at n=100, with 90th-percentile blanket size of 55.2 percent of n, and runtime of 10 milliseconds per patent. Difference against exact ground truth at n=12 is 0.088; difference against a high-sample Monte Carlo reference at n=100 is 0.062 plus or minus 0.003. A dense-component experiment shows that when 80 percent of patents share one component, the blanket correctly expands to cover that dense cluster, and the difference versus reference falls to 0.039 because the pooled computation becomes more accurate on homogeneous portfolios. Profit allocation proceeds hierarchically: exact Shapley distributes total profit among macro-components, then centrality-weighted Shapley distributes each component budget among covering patents. Estimating v(S) from real data is the primary open problem; we distinguish this from the computational contribution and outline a concrete roadmap for empirical validation using public ETSI, USPTO, and Lens.org datasets.

Joy Bose

Independent Researcher Bengaluru, India

Shapley Value Attribution