Procore: Robust Core-Set Selection Via Pareto Multi-Dimensional Optimization From Noisy Data

In large-scale, data-driven machine learning tasks, efficiently selecting representative subsets from noisy datasets is a key challenge for training efficiency and model robustness. Existing coreset selection methods typically rely on singleobjective criteria and lack principles to handle noise, leading to biased or unstable selections. To address this, we propose PROCore, a theoretically grounded solution for robust coreset selection from noisy data. PROCore integrates three key components: (1) structure-aware partitioning to decompose data into statistically stable substructures, (2) structure-alignment correction that leverages Mahalanobis and Wasserstein distances to adaptively reduce noise while preserving boundary samples, and (3) Pareto multi-objective optimization that jointly maximizes geometric coverage and gradient representativeness, with maximum-entropy tie-breaking to enhance diversity. We provide rigorous theoretical guarantees: a contraction-based convergence proof for noise correction, a bounded regret bound for entropybased selection, and a constant-factor approximation guarantee for the overall coreset quality. Experiments on five real-world datasets show that PROCore outperforms six state-of-the-art methods, achieving up to 2 percentage points higher F1 score under mixed noise. It maintains consistent robustness across noise levels, and accelerating coreset construction by 5×, demonstrating superior accuracy, robustness, and scalability.