Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2503.07966

Benign Overfitting and the Geometry of the Ridge Regression Solution in Binary Classification

Alexander Tsigler·Luiz F. O. Chamon·Spencer Frei·Peter L. Bartlett
View original source ↗Read source document ↗Export metadata ↓

Abstract

In this work, we investigate the behavior of ridge regression in an overparameterized binary classification task. We assume examples are drawn from (anisotropic) class-conditional cluster distributions with opposing means and we allow for the training labels to have a constant level of label-flipping noise. We characterize the classification error achieved by ridge regression under the assumption that the covariance matrix of the cluster distribution has a high effective rank in the tail. We show that ridge regression has qualitatively different behavior depending on the scale of the cluster mean vector and its interaction with the covariance matrix of the cluster distributions. In regimes where the scale is very large, the conditions that allow for benign overfitting turn out to be the same as those for the regression task. We additionally provide insights into how the introduction of label noise affects the behavior of the minimum norm interpolator (MNI). The optimal classifier in this setting is a linear transformation of the cluster mean vector and in the noiseless setting the MNI approximately learns this transformation. On the other hand, the introduction of label noise can significantly change the geometry of the solution while preserving the same qualitative behavior.

Explore related subjects

stat.MLcs.LG

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Alexander Tsigler, Luiz F. O. Chamon, Spencer Frei, Peter L. Bartlett. 2025-03-11. Benign Overfitting and the Geometry of the Ridge Regression Solution in Binary Classification. https://arxiv.org/abs/2503.07966

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Conditional Distributional Treatment Effects: Doubly Robust Estimation and Testing

Beyond conditional average treatment effects, treatments may impact the entire outcome distribution in covariate-dependent ways, for example, by altering the variance or tail risks for specific subpopulations. We propose a novel estimand to capture such conditional distributional treatment effects, and develop a doubly robust estimator that is minimax optimal in the local asymptotic sense. Using this, we develop a test for the global homogeneity of conditional potential outcome distributions that accommodates discrepancies beyond the maximum mean discrepancy (MMD), has provably valid type 1 error, and is consistent against fixed alternatives---the first test, to our knowledge, with such guarantees in this setting. We then provide a test that aggregates evidence across a grid of kernel-bandwidth choices. Furthermore, we derive exact closed-form expressions for two natural discrepancies (including the MMD), and provide a computationally efficient, permutation-free algorithm for our test.

stat.ML↗
arXiv2026

Flow Matching for Count Data

High-dimensional count data arise in applications such as single-cell RNA sequencing and neural spike trains, where mappings between distributions across successive batches or time points form critical components of data analysis. The recent success of diffusion- and flow-based deep generative models for images, video, and text motivates extending these ideas to count-valued settings, but many existing methods either treat each count as a categorical state or transform counts into a continuous space, neither of which is natural or efficient when the count range is large. We propose count-FM, a flow-matching framework for count data based on a continuous-time birth-death process with local unit jumps. Count-FM learns marginal transitions efficiently in count space through simulation-free training of conditional transition rates, allowing transport between arbitrary count-distributed source and target populations. In simulation, count-FM variants achieve strong sample quality while using substantially fewer parameters. We further apply count-FM to scRNA-seq and neural spike-train data for unconditional generation, transport, and conditional generation. Across these tasks, count-FM yields improved sample quality, greater modeling efficiency, and interpretable transport paths.

stat.ML↗
arXiv2026

Chaos Is a LADDER: Domain Generalization Beyond Invariance via Reweighting

Domain generalization (DG) aims to learn from multiple source domains and generalize to unseen target domains. Most DG methods pursue invariance: they seek a causal representation whose prediction rule is invariant across domains. This principle is effective when the causal mechanism is stable, but becomes restrictive when the domain itself modulates how causal content maps to the response. In this case, directly feeding domain style into the predictor can create misleading shortcuts, since style does not by itself cause the response. Yet the apparent chaos of multiple styles can become a ladder: style can locate the unseen target domain among source domains and guide which domain-dependent prediction rules should be trusted. We propose \emph{Latent Adaptive Domain Disentanglement and Environment Reweighting} (LADDER), a fixed-model DG pipeline that learns causal/style representations, freezes the encoders, fits source-specific classifiers, and uses an unlabeled target-domain covariate set only at inference to compute weights over these fixed classifiers, with no target labels or model-state updates. We establish theoretical guarantees for source reweighting and validate LADDER on simulations, FMoW, and a location-grouped iWildCam protocol, with gains in overall and group-averaged accuracy.

stat.ML↗