Tabular learning tasks often suffer from class imbalance, which is often addressed via weighting-based strategies. In this work, we compare the naive approach (unweighted) with the weighting-based rebalancing strategies. Somewhat surprisingly, we demonstrate that, asymptotically, as the predictor complexity increases with sample size, weighting strategies yield predictive performance identical to unweighted approaches across all evaluation metrics, up to a shift in the final threshold. To go beyond, we theoretically study the estimation of a linear regression function through weighted and unweighted CART trees with limited depths. In this setting, we prove that the points in the PR space for both strategies are distributed along the same curve, thus illustrating the similar nonasymptotic performance of the two strategies. Then, we numerically identify more complex synthetic settings where performance gaps, evaluated via fixed classifier complexity, favor weighting strategies. Thus, to guide practitioners, we introduce an indicator that aims at signaling whether a data set may benefit from weighting.
Classification and Regression Trees (CART) constitute one of the most influential paradigms in statistical learning. Although a variety of impurity measures have been proposed for different statistical models, these criteria are typically introduced on a case-by-case basis and analyzed separately. In this paper, we study CART through the lens of Bregman divergences. This perspective places the classical least-squares criterion, Poisson deviance, Kullback-Leibler-type losses, and other impurity measures associated with exponential-family models within a common framework. As a result, key ingredients of the CART methodology -- including node representatives, impurity measures, and split selection rules -- can be expressed and analyzed through general properties of convex functions rather than through separate model-specific constructions. Beyond the algorithmic formulation, we investigate theoretical properties of Bregman-based CART procedures. In particular, we analyze how geometric properties of the generating convex function influence impurity reductions and stability of recursive partitions. We also establish consistency results within the proposed framework, providing a unified theoretical treatment for a broad family of CART type procedures. Our results provide a geometric interpretation of impurity-based tree construction and show that many classical CART impurity criteria admit a common interpretation within a Bregman framework.
Mathias Bourel
IESTA, Facultad de Ciencias Económicas y de Administración, Universidad de la República, Uruguay · IRL-2030, Instituto Franco-Uruguayo de Matemática e Interacciones (IFUMI)
Class-level evaluation can conceal substantial performance disparities across subconcepts within the same class, causing models that perform well on average to fail on specific subpopulations. Prior work has shown that common evaluation measures for imbalanced classification are biased toward larger minority subconcepts and that utility-based reweighting using true subconcept labels can mitigate this bias; however, such labels are rarely available at test time. We introduce a practical utility-weighted evaluation that replaces unavailable subconcept labels with predicted posterior probabilities from a multiclass subconcept model. Evaluation weights are defined as the expected utility under this posterior, yielding a soft, uncertainty-aware metric we call predicted-weighted balanced accuracy (pBA). Experiments on tabular benchmarks as well as medical-imaging and text datasets show that unweighted scores can be misleading under within-class heterogeneity, while pBA provides more stable and interpretable assessments when subconcept distributions are uneven but not pathological. Our code is available at: https://anonymous.4open.science/r/correcting-bias-imbalance-9C6C/.
Loss reweighting is a widely used strategy for long-tailed classification, but existing reweighting strategies often rely on heuristics and rarely define a well-specified target. Inspired by Neural Collapse (NC), the ideal simplex Equiangular Tight Frame (ETF) terminal geometry suggests equal per-class average loss as a reasonable target for reweighting. Based on the ideal equal loss objective, we consider loss reweighting as an inverse problem and propose an inverse-view reweighting strategy that infers class weights dynamically to match this ideal objective. Empirically, NC metrics suggest our method can effectively reduce the loss imbalance coefficient and closer alignment with NC geometry while consistently outperforming strong long-tailed baselines on different datasets.
Jinping Wang, Zixin Tong, Zhiwu Xie +1
CSMT, Wenzhou-Kean University · International Frontier Interdisciplinary Research Institute, Wenzhou-Kean University