提出统一方法构造高精度数据压缩子集，适用多种复杂模型。
Accurate Coresets for Latent Variable Models and Regularized Regression
- 构建统一框架，适用于潜变量模型与正则化回归问题
- 潜变量模型核心集大小为多项式级别，正则化回归更小于输入维数的幂
- 实验验证理论优势，适合处理大规模数据建模任务
准确的核心集是原始数据集的加权子集，用其训练的模型能保持与全量数据训练相同精度。以往研究主要集中于少数模型。本文提出统一框架，实现通用问题的准确核心集构造，涵盖广泛潜变量模型和ℓ_p-正则化ℓ_p-回归。对于潜变量模型，核心集大小为O(poly(k))，k为潜变量数；对于ℓ_p-正则化ℓ_p-回归，算法利用正则化降低模型复杂度，核心集大小始终小于d^p（d为输入维度，λ>0）。该结果天然改进了岭回归的核心集规模。通过真实数据集上的大量实验验证了理论成果。
原文摘要 · Abstract (English)
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 $\ell_p$-regularized $\ell_p$-regression. For latent variable models, our coreset size is $O\left(\mathrm{poly}(k)\right)$, where $k$ is the number of latent variables. For $\ell_p$-regularized $\ell_p$-regression, our algorithm captures the reduction of model complexity due to regularization, resulting in a coreset whose size is always smaller than $d^{p}$ 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.
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