Deterministic Coreset Construction via Adaptive Sensitivity Trimming

TL;DR

This paper introduces a deterministic coreset construction method called ADUWT for empirical risk minimization, providing theoretical guarantees, optimality proofs, and practical algorithms for various models.

Contribution

The paper presents the ADUWT algorithm for deterministic coreset construction with data-dependent uniform weights and provides comprehensive theoretical analysis and practical sensitivity oracles.

Findings

Achieves uniform (1±ε) approximation for ERM objectives

Proves the optimality of adaptive weights via minimax characterization

Provides sensitivity oracles for kernel ridge regression, logistic regression, and SVM

Abstract

We develop a rigorous framework for deterministic coreset construction in empirical risk minimization (ERM). Our central contribution is the Adaptive Deterministic Uniform-Weight Trimming (ADUWT) algorithm, which constructs a coreset by excising points with the lowest sensitivity bounds and applying a data-dependent uniform weight to the remainder. The method yields a uniform $(1\pm\varepsilon)$ relative-error approximation for the ERM objective over the entire hypothesis space. We provide complete analysis, including (i) a minimax characterization proving the optimality of the adaptive weight, (ii) an instance-dependent size analysis in terms of a \emph{Sensitivity Heterogeneity Index}, and (iii) tractable sensitivity oracles for kernel ridge regression, regularized logistic regression, and linear SVM. Reproducibility is supported by precise pseudocode for the algorithm, sensitivity oracles, and evaluation pipeline. Empirical results align with the theory. We conclude with open problems on instance-optimal oracles, deterministic streaming, and fairness-constrained ERM.