# Accurate Coresets for Latent Variable Models and Regularized Regression

arXiv: https://arxiv.org/abs/2412.20189 · HTML: https://mlsanity.com/paper/2412.20189/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 28 references that are in the map.
- First posted on arXiv 28 Dec 2024.

## Builds on (most cited first, 12 of 12)

- [Turning Big data into tiny data: Constant-size coresets for k-means, PCA and projective clustering](https://mlsanity.com/paper/1807.04518/) (2018)
- [Dimensionality Reduction for k-Means Clustering and Low Rank Approximation](https://mlsanity.com/paper/1410.6801/) (2014)
- [Training Gaussian Mixture Models at Scale via Coresets](https://mlsanity.com/paper/1703.08110/) (2017)
- [Coresets for Near-Convex Functions](https://mlsanity.com/paper/2006.05482/) (2020)
- [A New Coreset Framework for Clustering](https://mlsanity.com/paper/2104.06133/) (2021)
- [Optimal approximate matrix product in terms of stable rank](https://mlsanity.com/paper/1507.02268/) (2015)
- [Coresets for Classification -- Simplified and Strengthened](https://mlsanity.com/paper/2106.04254/) (2021)
- [Towards Optimal Lower Bounds for k-median and k-means Coresets](https://mlsanity.com/paper/2202.12793/) (2022)
- [Sharper Bounds for Regularized Data Fitting](https://mlsanity.com/paper/1611.03225/) (2016)
- [Online Lewis Weight Sampling](https://mlsanity.com/paper/2207.08268/) (2022)
- [On Coresets For Regularized Regression](https://mlsanity.com/paper/2006.05440/) (2020)
- [Streaming Coresets for Symmetric Tensor Factorization](https://mlsanity.com/paper/2006.01225/) (2020)

## Built on by (most cited first, 1 of 1)

- [Deterministic Coreset for Lp Subspace](https://mlsanity.com/paper/2601.00361/) (2026)

## Abstract (arXiv)

Accurate coresets are a weighted subset of the original dataset, ensuring a model trained on the accurate coreset maintains the same level of accuracy as a model trained on the full dataset. Primarily, these coresets have been studied for a limited range of machine learning models. In this paper, we introduce a unified framework for constructing accurate coresets. Using this framework, we present accurate coreset construction algorithms for general problems, including a wide range of latent variable model problems and ℓp-regularized ℓp-regression. For latent variable models, our coreset size is Oleft(poly(k)right), where k is the number of latent variables. For ℓp-regularized ℓp-regression, our algorithm captures the reduction of model complexity due to regularization, resulting in a coreset whose size is always smaller than dp for a regularization parameter λ > 0. Here, d is the dimension of the input points. This inherently improves the size of the accurate coreset for ridge regression. We substantiate our theoretical findings with extensive experimental evaluations on real datasets.