Tree Ensemble Explainability through the Hoeffding Functional Decomposition and TreeHFD Algorithm

TL;DR

This paper introduces TreeHFD, an algorithm that estimates the Hoeffding functional decomposition for tree ensembles, enhancing explainability by providing sparse, orthogonal, and causal variable effects, with proven convergence and practical effectiveness.

Contribution

The paper presents TreeHFD, a novel method for estimating Hoeffding decompositions from data, addressing the challenge of explainability in tree ensemble models with dependent variables.

Findings

TreeHFD converges and maintains orthogonality and sparsity.

TreeHFD effectively identifies causal variables.

TreeSHAP is closely related to Hoeffding decomposition.

Abstract

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.