# Statistical Inference for Explainable Boosting Machines

arXiv: https://arxiv.org/abs/2601.18857 · HTML: https://mlsanity.com/paper/2601.18857/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 42 references that are in the map.
- First posted on arXiv 26 Jan 2026.

## Builds on (most cited first, 15 of 15)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [InterpretML: A Unified Framework for Machine Learning Interpretability](https://mlsanity.com/paper/1909.09223/) (2019)
- [Visualizing the Effects of Predictor Variables in Black Box Supervised Learning Models](https://mlsanity.com/paper/1612.08468/) (2016)
- [Unrestricted Permutation forces Extrapolation: Variable Importance Requires at least One More Model, or There Is No Free Variable Importance](https://mlsanity.com/paper/1905.03151/) (2019)
- [Shapley values for feature selection: The good, the bad, and the axioms](https://mlsanity.com/paper/2102.10936/) (2021)
- [Purifying Interaction Effects with the Functional ANOVA: An Efficient Algorithm for Recovering Identifiable Additive Models](https://mlsanity.com/paper/1911.04974/) (2019)
- [Minimax Optimal Rates of Estimation in High Dimensional Additive Models: Universal Phase Transition](https://mlsanity.com/paper/1503.02817/) (2015)
- [SGLB: Stochastic Gradient Langevin Boosting](https://mlsanity.com/paper/2001.07248/) (2020)
- [Boulevard: Regularized Stochastic Gradient Boosted Trees and Their Limiting Distribution](https://mlsanity.com/paper/1806.09762/) (2018)
- [The Infinitesimal Jackknife and Combinations of Models](https://mlsanity.com/paper/2209.00147/) (2022)
- [Gradient Boosting Performs Gaussian Process Inference](https://mlsanity.com/paper/2206.05608/) (2022)
- [Statistical Inference for Gradient Boosting Regression](https://mlsanity.com/paper/2509.23127/) (2025)

## Abstract (arXiv)

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.