Deterministic Coreset Construction via Adaptive Sensitivity Trimming
This work addresses the need for efficient and reliable data summarization in machine learning, offering a deterministic approach that is incremental over prior probabilistic methods.
The paper tackles the problem of deterministic coreset construction for empirical risk minimization by introducing the ADUWT algorithm, which achieves a uniform (1±ε) relative-error approximation with theoretical guarantees on optimality and instance-dependent size analysis.
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.