Woodelf++: A Fast and Unified Partial Dependence Plot Algorithm for Decision Tree Ensembles

2026-05-14

AI Summary

This work addresses the high computational complexity and poor scalability of existing partial dependence analysis methods. It proposes a unified framework based on pseudo-Boolean functions that, for the first time, enables efficient exact or approximate computation of partial dependence plots (PDPs), joint PDPs, arbitrary-order partial dependence interaction values (PDIVs), and a newly introduced Full PDP within a single architecture. By integrating decision tree structures with an extended Woodfold algorithm, the framework achieves exponential reductions in computational complexity and supports GPU acceleration. Experiments demonstrate that on a dataset with 400,000 samples, the proposed method computes PDPs and joint PDPs six times faster than the current state-of-the-art approach and five orders of magnitude faster than scikit-learn; moreover, it calculates any-order PDIVs in just five minutes—a task estimated to take over a million years with conventional methods.

Abstract

Partial Dependence Plots (PDPs) visualize how changes in a single feature affect the average model prediction. They are widely used in practice to interpret decision tree ensembles and other machine learning models. Joint-PDPs extend this idea to pairs of features, revealing their combined effect. Partial Dependence Interaction Values (PDIVs) measure feature interactions. The Any-Order-PDIVs task computes these interactions for every feature subset across all rows of the dataset. We introduce Woodelf++, a unified and efficient approach for computing all these useful explainability tools on decision tree ensembles, building on Woodelf, an algorithm for efficient SHAP computation. By deriving suitable metrics over pseudo-Boolean functions, Woodelf++ can compute PDPs (exact and approximate), Joint-PDPs, and Any-Order-PDIVs in a unified framework. Our method delivers substantial complexity improvements over the state of the art, including an exponential gain for Any-Order-PDIVs. Additionally, we introduce and efficiently compute Full PDPs, which leverage the model's split thresholds to faithfully capture its behavior across all possible feature values. Woodelf++ is implemented in pure Python and supports GPU acceleration. On a dataset with 400,000 rows, Woodelf++ computes PDP and Joint-PDP up to 6x faster than the state of the art and up to five orders of magnitude faster than scikit-learn. For Any-Order-PDIVs, the gap is even larger: Woodelf++ computes all interaction values in 5 minutes, while the state of the art is estimated to require over 1,000,000 years.

Problem

• Partial Dependence Plots
• Decision Tree Ensembles
• Feature Interaction
• Model Interpretability
• Any-Order-PDIVs

Innovation

• Partial Dependence Plots
• Decision Tree Ensembles
• Feature Interaction
• Any-Order-PDIVs
• Efficient Explainability