SAILS: Surrogate-based Analysis of Interactions via Local Effect Smooths

Feature interactions drive much of the predictive power of machine learning models, yet existing explanation methods only detect and quantify interactions without revealing their functional form, or visualize only restricted interaction types. We propose Surrogate-based Analysis of Interactions via Local effect Smooths (SAILS), a model-agnostic framework that analyzes pairwise interactions through interpretable generalized additive model (GAM) surrogates fitted to the local effects of a black-box model. For each interval of a feature of interest, the surrogate smooth terms isolate the interaction components on derivative level, enabling (i) interaction detection through a heuristic derived from significance tests on smooth terms, (ii) interaction form categorization into linear, product-separable, and non-product-separable types, and (iii) tailored, interpretable visualizations for each interaction type. We empirically validate the framework through controlled simulations and a real-world task, demonstrating its effectiveness for pairwise interactions, with limitations under strong feature correlations and higher-order interactions. SAILS fills a notable gap in the XAI toolbox, going beyond detection of interactions alone to characterizing their functional form.

Functional Decomposition and Shapley Interactions for Interpreting Survival Models

Hazard and survival functions are natural, interpretable targets in time-to-event prediction, but their inherent non-additivity fundamentally limits standard additive explanation methods. We introduce Survival Functional Decomposition (SurvFD), a principled approach for analyzing feature interactions in machine learning survival models. By decomposing higher-order effects into time-dependent and time-independent components, SurvFD offers a previously unrecognized perspective on survival explanations, explicitly characterizing when and why additive explanations fail. Building on this theoretical decomposition, we propose SurvSHAP-IQ, which extends Shapley interactions to time-indexed functions, providing a practical estimator for higher-order, time-dependent interactions. Together, SurvFD and SurvSHAP-IQ establish an interaction- and time-aware interpretability approach for survival modeling, with broad applicability across time-to-event prediction tasks.

GRANITE: A Generalized Regional Framework for Identifying Agreement in Feature-Based Explanations

Feature-based explanation methods aim to quantify how features influence the model's behavior, either locally or globally, but different methods often disagree, producing conflicting explanations. This disagreement arises primarily from two sources: how feature interactions are handled and how feature dependencies are incorporated. We propose GRANITE, a generalized regional explanation framework that partitions the feature space into regions where interaction and distribution influences are minimized. This approach aligns different explanation methods, yielding more consistent and interpretable explanations. GRANITE unifies existing regional approaches, extends them to feature groups, and introduces a recursive partitioning algorithm to estimate such regions. We demonstrate its effectiveness on real-world datasets, providing a practical tool for consistent and interpretable feature explanations.

Unifying Feature-Based Explanations with Functional ANOVA and Cooperative Game Theory

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.

Effector: A Python package for regional explanations

Global feature effect methods explain a model outputting one plot per feature. The plot shows the average effect of the feature on the output, like the effect of age on the annual income. However, average effects may be misleading when derived from local effects that are heterogeneous, i.e., they significantly deviate from the average. To decrease the heterogeneity, regional effects provide multiple plots per feature, each representing the average effect within a specific subspace. For interpretability, subspaces are defined as hyperrectangles defined by a chain of logical rules, like age's effect on annual income separately for males and females and different levels of professional experience. We introduce Effector, a Python library dedicated to regional feature effects. Effector implements well-established global effect methods, assesses the heterogeneity of each method and, based on that, provides regional effects. Effector automatically detects subspaces where regional effects have reduced heterogeneity. All global and regional effect methods share a common API, facilitating comparisons between them. Moreover, the library's interface is extensible so new methods can be easily added and benchmarked. The library has been thoroughly tested, ships with many tutorials (https://xai-effector.github.io/) and is available under an open-source license at PyPi (https://pypi.org/project/effector/) and Github (https://github.com/givasile/effector).

Explaining Bayesian Optimization by Shapley Values Facilitates Human-AI Collaboration

Bayesian optimization (BO) with Gaussian processes (GP) has become an indispensable algorithm for black box optimization problems. Not without a dash of irony, BO is often considered a black box itself, lacking ways to provide reasons as to why certain parameters are proposed to be evaluated. This is particularly relevant in human-in-the-loop applications of BO, such as in robotics. We address this issue by proposing ShapleyBO, a framework for interpreting BO's proposals by game-theoretic Shapley values.They quantify each parameter's contribution to BO's acquisition function. Exploiting the linearity of Shapley values, we are further able to identify how strongly each parameter drives BO's exploration and exploitation for additive acquisition functions like the confidence bound. We also show that ShapleyBO can disentangle the contributions to exploration into those that explore aleatoric and epistemic uncertainty. Moreover, our method gives rise to a ShapleyBO-assisted human machine interface (HMI), allowing users to interfere with BO in case proposals do not align with human reasoning. We demonstrate this HMI's benefits for the use case of personalizing wearable robotic devices (assistive back exosuits) by human-in-the-loop BO. Results suggest human-BO teams with access to ShapleyBO can achieve lower regret than teams without.

Leveraging Model-based Trees as Interpretable Surrogate Models for Model Distillation

Surrogate models play a crucial role in retrospectively interpreting complex and powerful black box machine learning models via model distillation. This paper focuses on using model-based trees as surrogate models which partition the feature space into interpretable regions via decision rules. Within each region, interpretable models based on additive main effects are used to approximate the behavior of the black box model, striking for an optimal balance between interpretability and performance. Four model-based tree algorithms, namely SLIM, GUIDE, MOB, and CTree, are compared regarding their ability to generate such surrogate models. We investigate fidelity, interpretability, stability, and the algorithms' capability to capture interaction effects through appropriate splits. Based on our comprehensive analyses, we finally provide an overview of user-specific recommendations.

Decomposing Global Feature Effects Based on Feature Interactions

Global feature effect methods, such as partial dependence plots, provide an intelligible visualization of the expected marginal feature effect. However, such global feature effect methods can be misleading, as they do not represent local feature effects of single observations well when feature interactions are present. We formally introduce generalized additive decomposition of global effects (GADGET), which is a new framework based on recursive partitioning to find interpretable regions in the feature space such that the interaction-related heterogeneity of local feature effects is minimized. We provide a mathematical foundation of the framework and show that it is applicable to the most popular methods to visualize marginal feature effects, namely partial dependence, accumulated local effects, and Shapley additive explanations (SHAP) dependence. Furthermore, we introduce a new permutation-based interaction test to detect significant feature interactions that is applicable to any feature effect method that fits into our proposed framework. We empirically evaluate the theoretical characteristics of the proposed methods based on various feature effect methods in different experimental settings. Moreover, we apply our introduced methodology to two real-world examples to showcase their usefulness.

REPID: Regional Effect Plots with implicit Interaction Detection

Machine learning models can automatically learn complex relationships, such as non-linear and interaction effects. Interpretable machine learning methods such as partial dependence plots visualize marginal feature effects but may lead to misleading interpretations when feature interactions are present. Hence, employing additional methods that can detect and measure the strength of interactions is paramount to better understand the inner workings of machine learning models. We demonstrate several drawbacks of existing global interaction detection approaches, characterize them theoretically, and evaluate them empirically. Furthermore, we introduce regional effect plots with implicit interaction detection, a novel framework to detect interactions between a feature of interest and other features. The framework also quantifies the strength of interactions and provides interpretable and distinct regions in which feature effects can be interpreted more reliably, as they are less confounded by interactions. We prove the theoretical eligibility of our method and show its applicability on various simulation and real-world examples.

Explaining Hyperparameter Optimization via Partial Dependence Plots

Automated hyperparameter optimization (HPO) can support practitioners to obtain peak performance in machine learning models. However, there is often a lack of valuable insights into the effects of different hyperparameters on the final model performance. This lack of explainability makes it difficult to trust and understand the automated HPO process and its results. We suggest using interpretable machine learning (IML) to gain insights from the experimental data obtained during HPO with Bayesian optimization (BO). BO tends to focus on promising regions with potential high-performance configurations and thus induces a sampling bias. Hence, many IML techniques, such as the partial dependence plot (PDP), carry the risk of generating biased interpretations. By leveraging the posterior uncertainty of the BO surrogate model, we introduce a variant of the PDP with estimated confidence bands. We propose to partition the hyperparameter space to obtain more confident and reliable PDPs in relevant sub-regions. In an experimental study, we provide quantitative evidence for the increased quality of the PDPs within sub-regions.