Discretization-free Multicalibration through Loss Minimization over Tree Ensembles
Hongyi Henry Jin, Zijun Ding, Dung Daniel Ngo, Zhiwei Steven Wu
TL;DR
This work addressing multicalibration avoids output discretization by post-processing a base predictor with a square-loss ERM over a depth-two tree ensemble, implemented via LightGBM. It provides a theoretical multicalibration guarantee under a loss-saturation assumption and empirically validates the approach across diverse tabular, image, and text datasets, showing it often matches or exceeds discretization-based baselines even when evaluated with discretized metrics. The method offers a practical, plug-in fairness enhancement that leverages standard tree-ensemble tools, reducing the need to tune discretization granularity and improving robustness to downstream discretization. Overall, the discretization-free approach broadens the applicability of multicalibration in real-world decision-making pipelines while maintaining competitive predictive performance.
Abstract
In recent years, multicalibration has emerged as a desirable learning objective for ensuring that a predictor is calibrated across a rich collection of overlapping subpopulations. Existing approaches typically achieve multicalibration by discretizing the predictor's output space and iteratively adjusting its output values. However, this discretization approach departs from the standard empirical risk minimization (ERM) pipeline, introduces rounding error and additional sensitive hyperparameter, and may distort the predictor's outputs in ways that hinder downstream decision-making. In this work, we propose a discretization-free multicalibration method that directly optimizes an empirical risk objective over an ensemble of depth-two decision trees. Our ERM approach can be implemented using off-the-shelf tree ensemble learning methods such as LightGBM. Our algorithm provably achieves multicalibration, provided that the data distribution satisfies a technical condition we term as loss saturation. Across multiple datasets, our empirical evaluation shows that this condition is always met in practice. Our discretization-free algorithm consistently matches or outperforms existing multicalibration approaches--even when evaluated using a discretization-based multicalibration metric that shares its discretization granularity with the baselines.