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

2026-04-12

AI Summary

This work addresses the scalability limitations of traditional Background SHAP methods on deep decision trees, where preprocessing complexity grows exponentially with tree depth (O(3^D)). To overcome this, the authors enhance the Woodelf algorithm by introducing a Strassen-like structured matrix multiplication, a fully vectorized non-recursive implementation, and a path-node merging strategy for identical features. These innovations reduce preprocessing complexity to O(2^D), substantially lowering computational and memory costs. The proposed method enables exact Background SHAP computation on trees up to depth 21 and achieves speedups of 33× and 162× on ensemble models with depths 12 and 15, respectively, significantly improving the scalability and efficiency of model interpretability for high-depth tree-based systems.

Technology Category

Machine Learning: Ensemble MethodsKnowledge Representation and Reasoning: Computational Complexity of ReasoningSearch and Optimization: Sampling/Simulation-based Search

Application Category

Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphsSearch and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for rankingUser Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

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.

Problem

• Background SHAP
• Decision Trees
• High Depth
• Scalability
• Interpretability

Innovation

• Background SHAP
• Decision Trees
• WoodelfHD
• Matrix-Vector Multiplication
• Interpretability