Georgia Institute of Technology College of Sciences

Sampling is a widely used algorithmic tool: running routines on a small representative subset of the data often leads to speedups while preserving accuracy. Recent works on algorithmic frameworks that relied on sampling graphs and matrices highlighted several connections between graph theory, statistics, optimization, and functional analysis. This talk will describe some key ideas that emerged from these connections: (1) Sampling as a generalized divide-and-conquer paradigm. (2) Implicit sampling without constructing the larger data set, and its algorithmic applications. (3)What does sampling need to preserve? What can sampling preserve? These ideas have applications in solvers for structured linear systems, network flow algorithms, input-sparsity time numerical routines, coresets, and dictionary learning.