Fast Estimation of Partial Dependence Functions using Trees
This work addresses the need for fast and reliable interpretation tools in machine learning, particularly for practitioners using tree-based models, though it is incremental as it builds on existing PD-based methods.
The paper tackles the problem of efficiently estimating Partial Dependence (PD) functions for interpreting machine learning models, proposing a new tree-based estimator called FastPD that improves computational complexity from quadratic to linear in the number of observations for moderately deep trees and provides consistent estimates unlike existing methods like TreeSHAP when features are correlated.
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 \texttt{TreeSHAP}. In this paper, we propose a new tree-based estimator, \texttt{FastPD}, which efficiently estimates arbitrary PD functions. We show that \texttt{FastPD} consistently estimates the desired population quantity -- in contrast to path-dependent \texttt{TreeSHAP} which is inconsistent when features are correlated. For moderately deep trees, \texttt{FastPD} improves the complexity of existing methods from quadratic to linear in the number of observations. By estimating PD functions for arbitrary feature subsets, \texttt{FastPD} can be used to extract PD-based interpretations such as SHAP, PD plots and higher-order interaction effects.