Hyperparameter optimization (HPO) is a crucial step in achieving strong predictive performance. Yet, the impact of individual hyperparameters on model generalization is highly context-dependent, prohibiting a one-size-fits-all solution and requiring opaque HPO methods to find optimal configurations. However, the black-box nature of most HPO methods undermines user trust and discourages adoption. To address this, we propose a game-theoretic explainability framework for HPO based on Shapley values and interactions. Our approach provides an additive decomposition of a performance measure across hyperparameters, enabling local and global explanations of hyperparameters' contributions and their interactions. The framework, named HyperSHAP, offers insights into ablation studies, the tunability of learning algorithms, and optimizer behavior across different hyperparameter spaces. We demonstrate HyperSHAP's capabilities on various HPO benchmarks to analyze the interaction structure of the corresponding HPO problems, demonstrating its broad applicability and actionable insights for improving HPO.

Abstract The Shapley value constitutes a widely recognized tool to assess individual contributions of cooperating entities from a game-theoretic perspective. Within the field of machine learning it is frequently applied to conduct feature attribution or data valuation. Aiming to overcome its deficiencies in capturing intricate interplay between entities, the Shapley interaction index represents a natural extension of the Shapley value, maintaining axiomatic uniqueness. As their complexity renders the exact computation of both quantities impractical, recent work transfers approximation approaches from the Shapley value to Shapley interactions. We propose Permutation-IQ , a domain-independent approximation method based on a novel representation that traces Shapley interactions back to the Shapley value’s fine-grained building blocks of marginal contributions. Sampling these instead of the coarser discrete derivatives of which Shapley interactions are composed, allows to utilize the collected information more efficiently.

Feature-based explanations, using perturbations or gradients, are a prevalent tool to understand decisions of black box machine learning models. Yet, differences between these methods still remain mostly unknown, which limits their applicability for practitioners. In this work, we introduce a unified framework for local and global feature-based explanations using two well-established concepts: functional ANOVA (fANOVA) from statistics, and the notion of value and interaction from cooperative game theory. We introduce three fANOVA decompositions that determine the influence of feature distributions, and use game-theoretic measures, such as the Shapley value and interactions, to specify the influence of higher-order interactions. Our framework combines these two dimensions to uncover similarities and differences between a wide range of explanation techniques for features and groups of features. We then empirically showcase the usefulness of our framework on synthetic and real-world datasets.

In unsupervised machine learning, Isolation Forest (IsoForest) is a widely used algorithm for the efficient detection of outliers.Identifying the features responsible for observed anomalies is crucial for practitioners, yet the ensemble nature of IsoForest complicates interpretation and comparison.As a remedy, SHAP is a prevalent method to interpret outlier scoring models by assigning contributions to individual features based on the Shapley Value (SV).However, complex anomalies typically involve interaction of features, and it is paramount for practitioners to distinguish such complex anomalies from simple cases.In this work, we propose Shapley Interactions (SIs) to enrich explanations of outliers with feature interactions.SIs, as an extension of the SV, decompose the outlier score into contributions of individual features and interactions of features up to a specified explanation order.We modify IsoForest to compute SI using TreeSHAP-IQ, an extension of TreeSHAP for tree-based models, using the shapiq package.Using a qualitative and quantitative analysis on synthetic and real-world datasets, we demonstrate the benefit of SI and feature interactions for outlier explanations over feature contributions alone.

Albeit the ubiquitous use of Graph Neural Networks (GNNs) in machine learning (ML) prediction tasks involving graph-structured data, their interpretability remains challenging. In explainable artificial intelligence (XAI), the Shapley Value (SV) is the predominant method to quantify contributions of individual features to a ML model’s output. Addressing the limitations of SVs in complex prediction models, Shapley Interactions (SIs) extend the SV to groups of features. In this work, we explain single graph predictions of GNNs with SIs that quantify node contributions and interactions among multiple nodes. By exploiting the GNN architecture, we show that the structure of interactions in node embeddings are preserved for graph prediction. As a result, the exponential complexity of SIs depends only on the receptive fields, i.e. the message-passing ranges determined by the connectivity of the graph and the number of convolutional layers. Based on our theoretical results, we introduce GraphSHAP-IQ, an efficient approach to compute any-order SIs exactly. GraphSHAP-IQ is applicable to popular message passing techniques in conjunction with a linear global pooling and output layer. We showcase that GraphSHAP-IQ substantially reduces the exponential complexity of computing exact SIs on multiple benchmark datasets. Beyond exact computation, we evaluate GraphSHAP-IQ’s approximation of SIs on popular GNN architectures and compare with existing baselines. Lastly, we visualize SIs of real-world water distribution networks and molecule structures using a SI-Graph.

Maximilian Spliethöver, Tim Knebler, Fabian Fumagalli, Maximilian Muschalik, Barbara Hammer, Eyke Hüllermeier, Henning Wachsmuth. Proceedings of the 2025 Conference of the Nations of the Americas Chapter of the Association for Computational Linguistics: Human Language Technologies (Volume 1: Long Papers). 2025.

Language-image pre-training (LIP) enables the development of vision-language models capable of zero-shot classification, localization, multimodal retrieval, and semantic understanding. Various explanation methods have been proposed to visualize the importance of input image-text pairs on the model's similarity outputs. However, popular saliency maps are limited by capturing only first-order attributions, overlooking the complex cross-modal interactions intrinsic to such encoders. We introduce faithful interaction explanations of LIP models (FIxLIP) as a unified approach to decomposing the similarity in vision-language encoders. FIxLIP is rooted in game theory, where we analyze how using the weighted Banzhaf interaction index offers greater flexibility and improves computational efficiency over the Shapley interaction quantification framework. From a practical perspective, we propose how to naturally extend explanation evaluation metrics, such as the pointing game and area between the insertion/deletion curves, to second-order interaction explanations. Experiments on the MS COCO and ImageNet-1k benchmarks validate that second-order methods, such as FIxLIP, outperform first-order attribution methods. Beyond delivering high-quality explanations, we demonstrate the utility of FIxLIP in comparing different models, e.g. CLIP vs. SigLIP-2.

The Shapley value, which is arguably the most popular approach for assigning a meaningful contribution value to players in a cooperative game, has recently been used intensively in explainable artificial intelligence. Its meaningfulness is due to axiomatic properties that only the Shapley value satisfies, which, however, comes at the expense of an exact computation growing exponentially with the number of agents. Accordingly, a number of works are devoted to the efficient approximation of the Shapley value, most of them revolve around the notion of an agent's marginal contribution. In this paper, we propose with SVARM and Stratified SVARM two parameter-free and domain-independent approximation algorithms based on a representation of the Shapley value detached from the notion of marginal contribution. We prove unmatched theoretical guarantees regarding their approximation quality and provide empirical results including synthetic games as well as common explainability use cases comparing ourselves with state-of-the-art methods.

While shallow decision trees may be interpretable, larger ensemble models like gradient-boosted trees, which often set the state of the art in machine learning problems involving tabular data, still remain black box models. As a remedy, the Shapley value (SV) is a well-known concept in explainable artificial intelligence (XAI) research for quantifying additive feature attributions of predictions. The model-specific TreeSHAP methodology solves the exponential complexity for retrieving exact SVs from tree-based models. Expanding beyond individual feature attribution, Shapley interactions reveal the impact of intricate feature interactions of any order. In this work, we present TreeSHAP-IQ, an efficient method to compute any-order additive Shapley interactions for predictions of tree-based models. TreeSHAP-IQ is supported by a mathematical framework that exploits polynomial arithmetic to compute the interaction scores in a single recursive traversal of the tree, akin to Linear TreeSHAP. We apply TreeSHAP-IQ on state-of-the-art tree ensembles and explore interactions on well-established benchmark datasets.

Addressing the limitations of individual attribution scores via the Shapley value (SV), the field of explainable AI (XAI) has recently explored intricate interactions of features or data points. In particular, extensions of the SV, such as the Shapley Interaction Index (SII), have been proposed as a measure to still benefit from the axiomatic basis of the SV. However, similar to the SV, their exact computation remains computationally prohibitive. Hence, we propose with SVARM-IQ a sampling-based approach to efficiently approximate Shapley-based interaction indices of any order. SVARM-IQ can be applied to a broad class of interaction indices, including the SII, by leveraging a novel stratified representation. We provide non-asymptotic theoretical guarantees on its approximation quality and empirically demonstrate that SVARM-IQ achieves state-of-the-art estimation results in practical XAI scenarios on different model classes and application domains.

The Shapley value (SV) is a prevalent approach of allocating credit to machine learning (ML) entities to understand black box ML models. Enriching such interpretations with higher-order interactions is inevitable for complex systems, where the Shapley Interaction Index (SII) is a direct axiomatic extension of the SV. While it is well-known that the SV yields an optimal approximation of any game via a weighted least square (WLS) objective, an extension of this result to SII has been a long-standing open problem, which even led to the proposal of an alternative index. In this work, we characterize higher-order SII as a solution to a WLS problem, which constructs an optimal approximation via SII and k-Shapley values (k-SII). We prove this representation for the SV and pairwise SII and give empirically validated conjectures for higher orders. As a result, we propose KernelSHAP-IQ, a direct extension of KernelSHAP for SII, and demonstrate state-of-the-art performance for feature interactions.

Originally rooted in game theory, the Shapley Value (SV) has recently become an important tool in machine learning research. Perhaps most notably, it is used for feature attribution and data valuation in explainable artificial intelligence. Shapley Interactions (SIs) naturally extend the SV and address its limitations by assigning joint contributions to groups of entities, which enhance understanding of black box machine learning models. Due to the exponential complexity of computing SVs and SIs, various methods have been proposed that exploit structural assumptions or yield probabilistic estimates given limited resources. In this work, we introduce shapiq, an open-source Python package that unifies state-of-the-art algorithms to efficiently compute SVs and any-order SIs in an application-agnostic framework. Moreover, it includes a benchmarking suite containing 11 machine learning applications of SIs with pre-computed games and ground-truth values to systematically assess computational performance across domains. For practitioners, shapiq is able to explain and visualize any-order feature interactions in predictions of models, including vision transformers, language models, as well as XGBoost and LightGBM with TreeSHAP-IQ. With shapiq, we extend shap beyond feature attributions and consolidate the application of SVs and SIs in machine learning that facilitates future research. The source code and documentation are available at https://github.com/mmschlk/shapiq.

Removal-based explanations are a general framework to provide feature importance scores, where feature removal, i.e. restricting a model on a subset of features, is a central component.While many machine learning applications require dynamic modeling environments, where distributions and models change over time, removal-based explanations and feature removal have mainly been considered in a static batch learning environment.Recently, an interventional and observational perturbation method was presented that allows to remove features efficiently in dynamic learning environments with concept drift.In this paper, we compare these two algorithms on two synthetic data streams.We showcase how both yield substantially different explanations when features are correlated and provide guidance on the choice based on the application.

Predominately in explainable artificial intelligence (XAI) research, the Shapley value (SV) is applied to determine feature attributions for any black box model. Shapley interaction indices extend the SV to define any-order feature interactions. Defining a unique Shapley interaction index is an open research question and, so far, three definitions have been proposed, which differ by their choice of axioms. Moreover, each definition requires a specific approximation technique. Here, we propose SHAPley Interaction Quantification (SHAP-IQ), an efficient sampling-based approximator to compute Shapley interactions for arbitrary cardinal interaction indices (CII), i.e. interaction indices that satisfy the linearity, symmetry and dummy axiom. SHAP-IQ is based on a novel representation and, in contrast to existing methods, we provide theoretical guarantees for its approximation quality, as well as estimates for the variance of the point estimates. For the special case of SV, our approach reveals a novel representation of the SV and corresponds to Unbiased KernelSHAP with a greatly simplified calculation. We illustrate the computational efficiency and effectiveness by explaining language, image classification and high-dimensional synthetic models.

Abstract Explainable artificial intelligence has mainly focused on static learning scenarios so far. We are interested in dynamic scenarios where data is sampled progressively, and learning is done in an incremental rather than a batch mode. We seek efficient incremental algorithms for computing feature importance (FI). Permutation feature importance (PFI) is a well-established model-agnostic measure to obtain global FI based on feature marginalization of absent features. We propose an efficient, model-agnostic algorithm called iPFI to estimate this measure incrementally and under dynamic modeling conditions including concept drift. We prove theoretical guarantees on the approximation quality in terms of expectation and variance. To validate our theoretical findings and the efficacy of our approaches in incremental scenarios dealing with streaming data rather than traditional batch settings, we conduct multiple experimental studies on benchmark data with and without concept drift.