Title: Differentially Private Lewis Weight Computation
Primary area: alignment, fairness, safety, privacy, and societal considerations
Keywords: Differential Privacy, Lewis Weight, Optimization

Abstract: Lewis weight is a row leverage score for data matrices. It allows selecting a small number of important rows to approximate the original matrix with provably small error. Computing Lewis weights has long been a key problem in optimization, machine learning, and large-scale data analysis. Despite the significant advancement in the computational efficiency of Lewis Weights, privacy concerns regarding the weight computation are naturally rising. In this work, we propose a privacy-preserving Lewis weight computation with high efficiency and a differential privacy (DP) guarantee. Our theoretical results clearly demonstrate the proposed algorithm's convergence and privacy assurances, providing an effective solution to the trade-off between utility and privacy in Lewis weight computation.