arXiv subjects

Giuseppe Casalicchio

Publications and source records attributed to Giuseppe Casalicchio.

At least 19 recordsLinked to original sources

arXiv2026

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 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, showing its effectiveness for pairwise interactions, with limitations under strong feature correlations and higher-order interactions. SAILS fills a notable gap in the eXplainable AI (XAI) toolbox, going beyond detecting interactions alone to characterizing their functional form.

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arXiv2026

Analyzing Error Sources in Global Feature Effect Estimation

Global feature effects such as partial dependence (PD) and accumulated local effects (ALE) plots are widely used to interpret black-box models. However, they are only estimates of true underlying effects, and their reliability depends on multiple sources of error. Despite the popularity of global feature effects, these error sources are largely unexplored. In particular, the practically relevant question of whether to use training or holdout data to estimate feature effects remains unanswered. We address this gap by providing a systematic, estimator-level analysis that disentangles sources of bias and variance for PD and ALE. To this end, we derive a mean-squared-error decomposition that separates model bias, estimation bias, model variance, and estimation variance, and analyze their dependence on model characteristics, data selection, and sample size. We validate our theoretical findings through an extensive simulation study across multiple data-generating processes, learners, estimation strategies (training data, validation data, and cross-validation), and sample sizes. Our results reveal that, while using holdout data is theoretically the cleanest, potential biases arising from the training data are empirically negligible and dominated by the impact of the usually higher sample size. The estimation variance depends on both the presence of interactions and the sample size, with ALE being particularly sensitive to the latter. Cross-validation-based estimation is a promising approach that reduces the model variance component, particularly for overfitting models. Our analysis provides a principled explanation of the sources of error in feature effect estimates and offers concrete guidance on choosing estimation strategies when interpreting machine learning models.

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arXiv2026

xplainfi: Feature Importance and Statistical Inference for Machine Learning in R

We introduce xplainfi, an R package built on top of the mlr3 ecosystem for global, loss-based feature importance methods for machine learning models. Various feature importance methods exist in R, but significant gaps remain, particularly regarding conditional importance methods and associated statistical inference procedures. The package implements permutation feature importance, conditional feature importance, relative feature importance, leave-one-covariate-out, and generalizations thereof, and both marginal and conditional Shapley additive global importance methods. It provides a modular conditional sampling architecture based on Gaussian distributions, adversarial random forests, conditional inference trees, and knockoff-based samplers, which enable conditional importance analysis for continuous and mixed data. Statistical inference is available through multiple approaches, including variance-corrected confidence intervals and the conditional predictive impact framework. We demonstrate that xplainfi produces importance scores consistent with existing implementations across multiple simulation settings and learner types, while offering competitive runtime performance. The package is available on CRAN and provides researchers and practitioners with a comprehensive toolkit for feature importance analysis and model interpretation in R.

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arXiv2026

CASHomon Sets: Efficient Rashomon Sets Across Multiple Model Classes and their Hyperparameters

Rashomon sets are model sets within one model class that perform nearly as well as a reference model from the same model class. They reveal the existence of alternative well-performing models, which may support different interpretations. This enables selecting models that match domain knowledge, hidden constraints, or user preferences. However, efficient construction methods currently exist for only a few model classes. Applied machine learning usually searches many model classes, and the best class is unknown beforehand. We therefore study Rashomon sets in the combined algorithm selection and hyperparameter optimization (CASH) setting and call them CASHomon sets. We propose TruVaRImp, a model-based active learning algorithm for level set estimation with an implicit threshold, and provide convergence guarantees. On synthetic and real-world datasets, TruVaRImp reliably identifies CASHomon sets members and matches or outperforms naive sampling, Bayesian optimization, classical and implicit level set estimation methods, and other baselines. Our analyses of predictive multiplicity and feature-importance variability across model classes question the common practice of interpreting data through a single model class.

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arXiv2026

Interpretability-by-Design with Accurate Locally Additive Models and Conditional Feature Effects

Generalized additive models (GAMs) offer interpretability through independent univariate feature effects but underfit when interactions are present in data. GA$^2$Ms add selected pairwise interactions which improves accuracy, but sacrifices interpretability and limits model auditing. We propose \emph{Conditionally Additive Local Models} (CALMs), a new model class, that balances the interpretability of GAMs with the accuracy of GA$^2$Ms. CALMs allow multiple univariate shape functions per feature, each active in different regions of the input space. These regions are defined independently for each feature as simple logical conditions (thresholds) on the features it interacts with. As a result, effects remain locally additive while varying across subregions to capture interactions. We further propose a principled distillation-based training pipeline that identifies homogeneous regions with limited interactions and fits interpretable shape functions via region-aware backfitting. Experiments on diverse classification and regression tasks show that CALMs consistently outperform GAMs and achieve accuracy comparable with GA$^2$Ms. Overall, CALMs offer a compelling trade-off between predictive accuracy and interpretability.

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arXiv2026

Optimal Transport Group Counterfactual Explanations

Group counterfactual explanations find a set of counterfactual instances to explain a group of input instances contrastively. However, existing methods either (i) optimize counterfactuals only for a fixed group and do not generalize to new group members, (ii) strictly rely on strong model assumptions (e.g., linearity) for tractability or/and (iii) poorly control the counterfactual group geometry distortion. We instead learn an explicit optimal transport map that sends any group instance to its counterfactual without re-optimization, minimizing the group's total transport cost. This enables generalization with fewer parameters, making it easier to interpret the common actionable recourse. For linear classifiers, we prove that functions representing group counterfactuals are derived via mathematical optimization, identifying the underlying convex optimization type (QP, QCQP, ...). Experiments show that they accurately generalize, preserve group geometry and incur only negligible additional transport cost compared to baseline methods. If model linearity cannot be exploited, our approach also significantly outperforms the baselines.

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arXiv2025

Effector: A Python package for regional explanations

Effector is a Python package for interpreting machine learning (ML) models that are trained on tabular data through global and regional feature effects. Global effects, like Partial Dependence Plot (PDP) and Accumulated Local Effects (ALE), are widely used for explaining tabular ML models due to their simplicity -- each feature's average influence on the prediction is summarized by a single 1D plot. However, when features are interacting, global effects can be misleading. Regional effects address this by partitioning the input space into disjoint subregions with minimal interactions within each and computing a separate regional effect per subspace. Regional effects are then visualized by a set of 1D plots per feature. Effector provides efficient implementations of state-of-the-art global and regional feature effects methods under a unified API. The package integrates seamlessly with major ML libraries like scikit-learn and PyTorch. It is designed to be modular and extensible, and comes with comprehensive documentation and tutorials. Effector is an open-source project publicly available on Github at https://github.com/givasile/effector.

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arXiv2025

On the Robustness of Global Feature Effect Explanations

We study the robustness of global post-hoc explanations for predictive models trained on tabular data. Effects of predictor features in black-box supervised learning are an essential diagnostic tool for model debugging and scientific discovery in applied sciences. However, how vulnerable they are to data and model perturbations remains an open research question. We introduce several theoretical bounds for evaluating the robustness of partial dependence plots and accumulated local effects. Our experimental results with synthetic and real-world datasets quantify the gap between the best and worst-case scenarios of (mis)interpreting machine learning predictions globally.

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arXiv2025

Privilege Scores

Bias-transforming methods of fairness-aware machine learning aim to correct a non-neutral status quo with respect to a protected attribute (PA). Current methods, however, lack an explicit formulation of what drives non-neutrality. We introduce privilege scores (PS) to measure PA-related privilege by comparing the model predictions in the real world with those in a fair world in which the influence of the PA is removed. At the individual level, PS can identify individuals who qualify for affirmative action; at the global level, PS can inform bias-transforming policies. After presenting estimation methods for PS, we propose privilege score contributions (PSCs), an interpretation method that attributes the origin of privilege to mediating features and direct effects. We provide confidence intervals for both PS and PSCs. Experiments on simulated and real-world data demonstrate the broad applicability of our methods and provide novel insights into gender and racial privilege in mortgage and college admissions applications.

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arXiv2025

Efficient and Accurate Explanation Estimation with Distribution Compression

We discover a theoretical connection between explanation estimation and distribution compression that significantly improves the approximation of feature attributions, importance, and effects. While the exact computation of various machine learning explanations requires numerous model inferences and becomes impractical, the computational cost of approximation increases with an ever-increasing size of data and model parameters. We show that the standard i.i.d. sampling used in a broad spectrum of algorithms for post-hoc explanation leads to an approximation error worthy of improvement. To this end, we introduce Compress Then Explain (CTE), a new paradigm of sample-efficient explainability. It relies on distribution compression through kernel thinning to obtain a data sample that best approximates its marginal distribution. CTE significantly improves the accuracy and stability of explanation estimation with negligible computational overhead. It often achieves an on-par explanation approximation error 2-3x faster by using fewer samples, i.e. requiring 2-3x fewer model evaluations. CTE is a simple, yet powerful, plug-in for any explanation method that now relies on i.i.d. sampling.

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arXiv2024

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 and validate a new permutation-based interaction detection procedure 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 three real-world examples to showcase their usefulness.

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arXiv2024

fmeffects: An R Package for Forward Marginal Effects

Forward marginal effects have recently been introduced as a versatile and effective model-agnostic interpretation method particularly suited for non-linear and non-parametric prediction models. They provide comprehensible model explanations of the form: if we change feature values by a pre-specified step size, what is the change in the predicted outcome? We present the R package fmeffects, the first software implementation of the theory surrounding forward marginal effects. The relevant theoretical background, package functionality and handling, as well as the software design and options for future extensions are discussed in this paper.

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arXiv2024

Position Paper: Bridging the Gap Between Machine Learning and Sensitivity Analysis

We argue that interpretations of machine learning (ML) models or the model-building process can be seen as a form of sensitivity analysis (SA), a general methodology used to explain complex systems in many fields such as environmental modeling, engineering, or economics. We address both researchers and practitioners, calling attention to the benefits of a unified SA-based view of explanations in ML and the necessity to fully credit related work. We bridge the gap between both fields by formally describing how (a) the ML process is a system suitable for SA, (b) how existing ML interpretation methods relate to this perspective, and (c) how other SA techniques could be applied to ML.

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arXiv2024

A Guide to Feature Importance Methods for Scientific Inference

While machine learning (ML) models are increasingly used due to their high predictive power, their use in understanding the data-generating process (DGP) is limited. Understanding the DGP requires insights into feature-target associations, which many ML models cannot directly provide due to their opaque internal mechanisms. Feature importance (FI) methods provide useful insights into the DGP under certain conditions. Since the results of different FI methods have different interpretations, selecting the correct FI method for a concrete use case is crucial and still requires expert knowledge. This paper serves as a comprehensive guide to help understand the different interpretations of global FI methods. Through an extensive review of FI methods and providing new proofs regarding their interpretation, we facilitate a thorough understanding of these methods and formulate concrete recommendations for scientific inference. We conclude by discussing options for FI uncertainty estimation and point to directions for future research aiming at full statistical inference from black-box ML models.

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arXiv2024

Position: Why We Must Rethink Empirical Research in Machine Learning

We warn against a common but incomplete understanding of empirical research in machine learning that leads to non-replicable results, makes findings unreliable, and threatens to undermine progress in the field. To overcome this alarming situation, we call for more awareness of the plurality of ways of gaining knowledge experimentally but also of some epistemic limitations. In particular, we argue most current empirical machine learning research is fashioned as confirmatory research while it should rather be considered exploratory.

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arXiv2024

mlr3summary: Concise and interpretable summaries for machine learning models

This work introduces a novel R package for concise, informative summaries of machine learning models. We take inspiration from the summary function for (generalized) linear models in R, but extend it in several directions: First, our summary function is model-agnostic and provides a unified summary output also for non-parametric machine learning models; Second, the summary output is more extensive and customizable -- it comprises information on the dataset, model performance, model complexity, model's estimated feature importances, feature effects, and fairness metrics; Third, models are evaluated based on resampling strategies for unbiased estimates of model performances, feature importances, etc. Overall, the clear, structured output should help to enhance and expedite the model selection process, making it a helpful tool for practitioners and researchers alike.

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arXiv2024

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.

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arXiv2023

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.

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