The functional ANOVA, or Hoeffding decomposition, provides a principled framework for interpretability by decomposing a model prediction into main effects and higher-order interactions. For independent inputs, this classical decomposition is explicit. It is closely connected to SHAP values, generalized additive models, and orthogonal polynomial expansions, and therefore constitutes a fundamental tool for additive explainability. In the more general and realistic dependent setting, however, obtaining a tractable representation and estimating the decomposition from data remain challenging. In this work, we address this problem for continuous inputs. By combining Hilbert space methods with the generalized functional ANOVA, we build an explicit decomposition Riesz Basis allowing to easily compute the decomposition. Our formulation recovers the classical independent case and its associated orthogonal decomposition. Building on this representation, we propose a simple but mighty algorithm to estimate the decomposition from a data sample in a model-agnostic setting and we compare it empirically with several state-of-the-art explanation methods, demonstrating the power of the approach.

Decision trees are well-known due to their ease of interpretability. To improve accuracy, we need to grow deep trees or ensembles of trees. These are hard to interpret, offsetting their original benefits. Shapley values have recently become a popular way to explain the predictions of tree-based machine learning models. It provides a linear weighting to features independent of the tree structure. The rise in popularity is mainly due to TreeShap, which solves a general exponential complexity problem in polynomial time. Following extensive adoption in the industry, more efficient algorithms are required. This paper presents a more efficient and straightforward algorithm: Linear TreeShap. Like TreeShap, Linear TreeShap is exact and requires the same amount of memory.

Decision trees are well-known due to their ease of interpretability.To improve accuracy, we need to grow deep trees or ensembles of trees.These are hard to interpret, offsetting their original benefits. Shapley values have recently become a popular way to explain the predictions of tree-based machine learning models. It provides a linear weighting to features independent of the tree structure. The rise in popularity is mainly due to TreeShap, which solves a general exponential complexity problem in polynomial time. Following extensive adoption in the industry, more efficient algorithms are required. This paper presents a more efficient and straightforward algorithm: Linear TreeShap.Like TreeShap, Linear TreeShap is exact and requires the same amount of memory.

Tree ensembles have demonstrated state-of-the-art predictive performance across a wide range of problems involving tabular data. Nevertheless, the black-box nature of tree ensembles is a strong limitation, especially for applications with critical decisions at stake. The Hoeffding or ANOVA functional decomposition is a powerful explainability method, as it breaks down black-box models into a unique sum of lower-dimensional functions, provided that input variables are independent. In standard learning settings, input variables are often dependent, and the Hoeffding decomposition is generalized through hierarchical orthogonality constraints. Such generalization leads to unique and sparse decompositions with well-defined main effects and interactions. However, the practical estimation of this decomposition from a data sample is still an open problem. Therefore, we introduce the TreeHFD algorithm to estimate the Hoeffding decomposition of a tree ensemble from a data sample. We show the convergence of TreeHFD, along with the main properties of orthogonality, sparsity, and causal variable selection. The high performance of TreeHFD is demonstrated through experiments on both simulated and real data, using our treehfd Python package (https://github.com/ThalesGroup/treehfd). Besides, we empirically show that the widely used TreeSHAP method, based on Shapley values, is strongly connected to the Hoeffding decomposition.

Most explainable AI (XAI) frameworks are limited in their expressiveness, summarizing complex feature effects as single scalar values ϕ_i. This approach answers "what" features are important but fails to reveal "how" they interact. Furthermore, methods that attempt to capture interactions, like those based on Shapley values, often face an exponential computational cost. We present STRIDE, a scalable framework that addresses both limitations by reframing explanation as a subset-enumeration-free, orthogonal "functional decomposition" in a Reproducing Kernel Hilbert Space (RKHS). In the tabular setups we study, STRIDE analytically computes functional components f_S(x_S) via a recursive kernel-centering procedure. The approach is model-agnostic and theoretically grounded with results on orthogonality and L^2 convergence. In tabular benchmarks (10 datasets, median over 10 seeds), STRIDE attains a 3.0 times median speedup over TreeSHAP and a mean R^2=0.93 for reconstruction. We also introduce "component surgery", a diagnostic that isolates a learned interaction and quantifies its contribution; on California Housing, removing a single interaction reduces test R^2 from 0.019 to 0.027.

The field of health informatics has been profoundly influenced by the development of random forest models, which have led to significant advances in the interpretability of feature interactions. These models are characterized by their robustness to overfitting and parallelization, making them particularly useful in this domain. However, the increasing number of features and estimators in random forests can prevent domain experts from accurately interpreting global feature interactions, thereby compromising trust and regulatory compliance. A method called the surrogate interpretability graph has been developed to address this issue. It uses graphs and mixed-integer linear programming to analyze and visualize feature interactions. This improves their interpretability by visualizing the feature usage per decision-feature-interaction table and the most dominant hierarchical decision feature interactions for predictions. The implementation of a surrogate interpretable graph enhances global interpretability, which is critical for such a high-stakes domain.

Decision trees are well-known due to their ease of interpretability.To improve accuracy, we need to grow deep trees or ensembles of trees.These are hard to interpret, offsetting their original benefits. Shapley values have recently become a popular way to explain the predictions of tree-based machine learning models. It provides a linear weighting to features independent of the tree structure. The rise in popularity is mainly due to TreeShap, which solves a general exponential complexity problem in polynomial time. Following extensive adoption in the industry, more efficient algorithms are required.

Shapley values have been used extensively in machine learning, not only to explain black box machine learning models, but among other tasks, also to conduct model debugging, sensitivity and fairness analyses and to select important features for robust modelling and for further follow-up analyses. Shapley values satisfy certain axioms that promote fairness in distributing contributions of features toward prediction or reducing error, after accounting for non-linear relationships and interactions when complex machine learning models are employed. Recently, a number of feature selection methods utilising Shapley values have been introduced. Here, we present a novel feature selection method, LLpowershap, which makes use of loss-based Shapley values to identify informative features with minimal noise among the selected sets of features. Our simulation results show that LLpowershap not only identifies higher number of informative features but outputs fewer noise features compared to other state-of-the-art feature selection methods. Benchmarking results on four real-world datasets demonstrate higher or at par predictive performance of LLpowershap compared to other Shapley based wrapper methods, or filter methods.