---
title: "A Fast and Unified Partial Dependence Plot Algorithm"
authors:
  - "Ron Wettenstein"
  - "Alexander Nadel"
  - "Udi Boker"
doi: "10.24963/ijcai.2026/562"
url: "https://ijcai.org/proceedings/2026/562"
pdf: "https://ijcai.org/proceedings/2026/0562.pdf"
venue: "Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence"
year: 2026
pages: "5048-5056"
track: "Main Track"
keywords:
  - "Machine Learning: Explainable/Interpretable machine learning"
  - "Machine Learning: Game Theory"
  - "Machine Learning: Ensemble methods"
---

# A Fast and Unified Partial Dependence Plot Algorithm

Ron Wettenstein, Alexander Nadel, Udi Boker

*Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence*, pages 5048-5056. DOI: [10.24963/ijcai.2026/562](https://doi.org/10.24963/ijcai.2026/562)

## 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.