# On Coresets For Regularized Regression

arXiv: https://arxiv.org/abs/2006.05440 · HTML: https://mlsanity.com/paper/2006.05440/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jun 2020.

## Built on by (most cited first, 10 of 10)

- [DeepCore: A Comprehensive Library for Coreset Selection in Deep Learning](https://mlsanity.com/paper/2204.08499/) (2022)
- [Coresets for Vertical Federated Learning: Regularized Linear Regression and K-Means Clustering](https://mlsanity.com/paper/2210.14664/) (2022)
- [Provable Data Subset Selection For Efficient Neural Network Training](https://mlsanity.com/paper/2303.05151/) (2023)
- [A Novel Sequential Coreset Method for Gradient Descent Algorithms](https://mlsanity.com/paper/2112.02504/) (2021)
- [Evolution-aware VAriance (EVA) Coreset Selection for Medical Image Classification](https://mlsanity.com/paper/2406.05677/) (2024)
- [DataS^3: Dataset Subset Selection for Specialization](https://mlsanity.com/paper/2504.16277/) (2025)
- [Accurate Coresets for Latent Variable Models and Regularized Regression](https://mlsanity.com/paper/2412.20189/) (2024)
- [Efficient NTK using Dimensionality Reduction](https://mlsanity.com/paper/2210.04807/) (2022)
- [Deterministic Coreset for Lp Subspace](https://mlsanity.com/paper/2601.00361/) (2026)
- [COREKG: Coreset-Guided Personalized Summarization of Knowledge Graphs](https://mlsanity.com/paper/2605.14900/) (2026)

## Abstract (arXiv)

We study the effect of norm based regularization on the size of coresets for regression problems. Specifically, given a matrix  A ∈ ℝn × d with ngg 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 neq 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.