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 $\lambda > 0$. 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.

A coreset (or core-set) of an input set is its small summation, such that solving a problem on the coreset as its input, provably yields the same result as solving the same problem on the original (full) set, for a given family of problems (models, classifiers, loss functions). Over the past decade, coreset construction algorithms have been suggested for many fundamental problems in e.g. machine/deep learning, computer vision, graphics, databases, and theoretical computer science. This introductory paper was written following requests from (usually non-expert, but also colleagues) regarding the many inconsistent coreset definitions, lack of available source code, the required deep theoretical background from different fields, and the dense papers that make it hard for beginners to apply coresets and develop new ones. The paper provides folklore, classic and simple results including step-by-step proofs and figures, for the simplest (accurate) coresets of very basic problems, such as: sum of vectors, minimum enclosing ball, SVD/ PCA and linear regression. Nevertheless, we did not find most of their constructions in the literature. Moreover, we expect that putting them together in a retrospective context would help the reader to grasp modern results that usually extend and generalize these fundamental observations. Experts might appreciate the unified notation and comparison table that links between existing results. Open source code with example scripts are provided for all the presented algorithms, to demonstrate their practical usage, and to support the readers who are more familiar with programming than math.