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

arXiv: https://arxiv.org/abs/2605.14578 · HTML: https://mlsanity.com/paper/2605.14578/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 28 references that are in the map.
- First posted on arXiv 14 May 2026.

## Builds on (most cited first, 9 of 9)

- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Visualizing the Effects of Predictor Variables in Black Box Supervised Learning Models](https://mlsanity.com/paper/1612.08468/) (2016)
- [Unifying local and global model explanations by functional decomposition of low dimensional structures](https://mlsanity.com/paper/2208.06151/) (2022)
- [On the Trustworthiness of Tree Ensemble Explainability Methods](https://mlsanity.com/paper/2110.00086/) (2021)
- [PiML Toolbox for Interpretable Machine Learning Model Development and Diagnostics](https://mlsanity.com/paper/2305.04214/) (2023)
- [iPDP: On Partial Dependence Plots in Dynamic Modeling Scenarios](https://mlsanity.com/paper/2306.07775/) (2023)
- [Fast Estimation of Partial Dependence Functions using Trees](https://mlsanity.com/paper/2410.13448/) (2024)
- [From Decision Trees to Boolean Logic: A Fast and Unified SHAP Algorithm](https://mlsanity.com/paper/2511.09376/) (2025)
- [Technical Report: Partial Dependence through Stratification](https://mlsanity.com/paper/1907.06698/) (2019)

## Abstract (arXiv)

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.