WOODELF-HD: Efficient Background SHAP for High-Depth Decision Trees

TL;DR

WoodelfHD significantly improves the efficiency of Background SHAP explanations for deep decision trees by reducing computational complexity and memory usage, enabling practical explanations for trees up to depth 21.

Contribution

It introduces a Strassen-like multiplication scheme and path node merging techniques to reduce complexity from 3^D to 2^D, enabling scalable exact SHAP explanations for deep trees.

Findings

Enables exact Background SHAP for trees up to depth 21.

Achieves 33x and 162x speedups on ensembles of depths 12 and 15.

Reduces memory usage and cache size through path node merging.

Abstract

Decision-tree ensembles are a cornerstone of predictive modeling, and SHAP is a standard framework for interpreting their predictions. Among its variants, Background SHAP offers high accuracy by modeling missing features using a background dataset. Historically, this approach did not scale well, as the time complexity for explaining n instances using m background samples included an O(mn) component. Recent methods such as Woodelf and PLTreeSHAP reduce this to O(m+n), but introduce a preprocessing bottleneck that grows as 3^D with tree depth D, making them impractical for deep trees. We address this limitation with WoodelfHD, a Woodelf extension that reduces the 3^D factor to 2^D. The key idea is a Strassen-like multiplication scheme that exploits the structure of Woodelf matrices, reducing matrix-vector multiplication from O(k^2) to O(k*log(k)) via a fully vectorized, non-recursive implementation. In addition, we merge path nodes with identical features, reducing cache size and memory usage. When running on standard environments, WoodelfHD enables exact Background SHAP computation for trees with depths up to 21, where previous methods fail due to excessive memory usage. For ensembles of depths 12 and 15, it achieves speedups of 33x and 162x, respectively, over the state-of-the-art.