Bayesian Coresets

<jats:title>Abstract</jats:title> <jats:p> Bayesian inference with modern, high‐volume data often becomes bottlenecked not by model complexity but by the repeated evaluation of a likelihood that factorizes into a potentially large number of per‐observation terms. <jats:italic>Bayesian coresets</jats:italic> address this bottleneck by replacing the full‐data log‐likelihood with a surrogate constructed from a <jats:italic>sparse, nonnegative weighted subset</jats:italic> of data points, yielding an approximate posterior that can be sampled or optimized using standard inference algorithms at a cost proportional to the coreset size rather than the full dataset size. This article reviews the basic problem setup, formal definitions, construction principles, representative algorithms and the main types of theoretical guarantees these algorithms come with. </jats:p>