# Fast Estimation of Partial Dependence Functions using Trees

arXiv: https://arxiv.org/abs/2410.13448 · HTML: https://mlsanity.com/paper/2410.13448/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 35 references that are in the map.
- First posted on arXiv 17 Oct 2024.

## Builds on (most cited first, 17 of 17)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Visualizing the Effects of Predictor Variables in Black Box Supervised Learning Models](https://mlsanity.com/paper/1612.08468/) (2016)
- [OpenML Benchmarking Suites](https://mlsanity.com/paper/1708.03731/) (2017)
- [Feature relevance quantification in explainable AI: A causal problem](https://mlsanity.com/paper/1910.13413/) (2019)
- [True to the Model or True to the Data?](https://mlsanity.com/paper/2006.16234/) (2020)
- [FastSHAP: Real-Time Shapley Value Estimation](https://mlsanity.com/paper/2107.07436/) (2021)
- [Explaining Deep Neural Networks with a Polynomial Time Algorithm for Shapley Values Approximation](https://mlsanity.com/paper/1903.10992/) (2019)
- [Nonparametric methods for doubly robust estimation of continuous treatment effects](https://mlsanity.com/paper/1507.00747/) (2015)
- [From Shapley Values to Generalized Additive Models and back](https://mlsanity.com/paper/2209.04012/) (2022)
- [Purifying Interaction Effects with the Functional ANOVA: An Efficient Algorithm for Recovering Identifiable Additive Models](https://mlsanity.com/paper/1911.04974/) (2019)
- [Beyond TreeSHAP: Efficient Computation of Any-Order Shapley Interactions for Tree Ensembles](https://mlsanity.com/paper/2401.12069/) (2024)
- [Fast TreeSHAP: Accelerating SHAP Value Computation for Trees](https://mlsanity.com/paper/2109.09847/) (2021)
- [Relating the Partial Dependence Plot and Permutation Feature Importance to the Data Generating Process](https://mlsanity.com/paper/2109.01433/) (2021)
- [Unifying local and global model explanations by functional decomposition of low dimensional structures](https://mlsanity.com/paper/2208.06151/) (2022)
- [Accelerating Shapley Explanation via Contributive Cooperator Selection](https://mlsanity.com/paper/2206.08529/) (2022)
- [Statistical Aspects of SHAP: Functional ANOVA for Model Interpretation](https://mlsanity.com/paper/2208.09970/) (2022)
- [Manifold Restricted Interventional Shapley Values](https://mlsanity.com/paper/2301.04041/) (2023)

## Built on by (most cited first, 4 of 4)

- [Quadrature-TreeSHAP: Depth-Independent TreeSHAP and Shapley Interactions](https://mlsanity.com/paper/2605.04497/) (2026)
- [Do covariates explain why these groups differ? The choice of reference group can reverse conclusions in the Oaxaca-Blinder decomposition](https://mlsanity.com/paper/2603.29972/) (2026)
- [Woodelf++: A Fast and Unified Partial Dependence Plot Algorithm for Decision Tree Ensembles](https://mlsanity.com/paper/2605.14578/) (2026)
- [Beyond Additive Decompositions: Interpretability Through Separability](https://mlsanity.com/paper/2605.31200/) (2026)

## Abstract (arXiv)

Many existing interpretation methods are based on Partial Dependence (PD) functions that, for a pre-trained machine learning model, capture how a subset of the features affects the predictions by averaging over the remaining features. Notable methods include Shapley additive explanations (SHAP) which computes feature contributions based on a game theoretical interpretation and PD plots (i.e., 1-dim PD functions) that capture average marginal main effects. Recent work has connected these approaches using a functional decomposition and argues that SHAP values can be misleading since they merge main and interaction effects into a single local effect. However, a major advantage of SHAP compared to other PD-based interpretations has been the availability of fast estimation techniques, such as textttTreeSHAP. In this paper, we propose a new tree-based estimator, textttFastPD, which efficiently estimates arbitrary PD functions. We show that textttFastPD consistently estimates the desired population quantity -- in contrast to path-dependent textttTreeSHAP which is inconsistent when features are correlated. For moderately deep trees, textttFastPD improves the complexity of existing methods from quadratic to linear in the number of observations. By estimating PD functions for arbitrary feature subsets, textttFastPD can be used to extract PD-based interpretations such as SHAP, PD plots and higher-order interaction effects.