Statistical Inference for Explainable Boosting Machines

TL;DR

This paper introduces a statistical inference framework for explainable boosting machines, enabling efficient uncertainty quantification and confidence intervals for feature effects without intensive bootstrapping.

Contribution

It develops asymptotically normal prediction methods for EBMs using kernel ridge regression, providing theoretical guarantees and runtime-efficient confidence intervals.

Findings

Achieves minimax-optimal MSE for Lipschitz GAMs with O(p n^{-2/3}) error.

Constructs runtime-efficient prediction and confidence intervals.

Provides theoretical guarantees for inference in EBMs.

Abstract

Explainable boosting machines (EBMs) are popular "glass-box" models that learn a set of univariate functions using boosting trees. These achieve explainability through visualizations of each feature's effect. However, unlike linear model coefficients, uncertainty quantification for the learned univariate functions requires computationally intensive bootstrapping, making it hard to know which features truly matter. We provide an alternative using recent advances in statistical inference for gradient boosting, deriving methods for statistical inference as well as end-to-end theoretical guarantees. Using a moving average instead of a sum of trees (Boulevard regularization) allows the boosting process to converge to a feature-wise kernel ridge regression. This produces asymptotically normal predictions that achieve the minimax-optimal MSE for fitting Lipschitz GAMs with $p$ features of $O(p n^{-2/3})$, successfully avoiding the curse of dimensionality. We then construct prediction intervals for the response and confidence intervals for each learned univariate function with a runtime independent of the number of datapoints, enabling further explainability within EBMs. Code is available at https://github.com/hetankevin/ebm-inference.