2020/06/09 by Rachit Chhaya, Chhaya, Rachit, Anirban Dasgupta +3 · 2 citations
Computer Science · Engineering · Mathematics · #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #Face and Expression Recognition #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Sparse and Compressive Sensing Techniques #Stochastic Gradient Optimization Techniques #cs.DS #cs.LG #stat.ML
paper · pdf · doi:10.48550/arxiv.2006.05440
Accepted at ICML 2020. Acknowledgements added. Minor errors fixed
openalex publication_date 2020/06/09 · arxiv created 2020/06/30 · arxiv updated 2020/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the effect of norm based regularization on the size of coresets for regression problems. Specifically, given a matrix A ∈ ℝn × d with n≫ d and a vector b ∈ ℝ ^ n and λ> 0, we analyze the size of coresets for regularized versions of regression of the form ‖Ax-b‖pr + λ‖x‖qs . Prior work has shown that for ridge regression (where p,q,r,s=2) we can obtain a coreset that is smaller than the coreset for the unregularized counterpart i.e. least squares regression (Avron et al). We show that when r ≠ s, no coreset for regularized regression can have size smaller than the optimal coreset of the unregularized version. The well known lasso problem falls under this category and hence does not allow a coreset smaller than the one for least squares regression. We propose a modified version of the lasso problem and obtain for it a coreset of size smaller than the least square regression. We empirically show that the modified version of lasso also induces sparsity in solution, similar to the original lasso. We also obtain smaller coresets for ℓp regression with ℓp regularization. We extend our methods to multi response regularized regression. Finally, we empirically demonstrate the coreset performance for the modified lasso and the ℓ1 regression with ℓ1 regularization.