An adaptive randomized pivoting strategy for low-rank approximation

Alice Cortinovis presents Adaptive Randomized Pivoting for selecting representative matrix columns through adaptive leverage-score sampling. Its expected Frobenius approximation error matches the optimal existence guarantee. The method is a randomized counterpart to an approach by Osinsky and offers a simpler, less costly alternative to volume sampling with the same theoretical guarantee. The talk extends the strategy to the Discrete Empirical Interpolation Method, cross or skeleton approximation, and Nyström approximation of positive-semidefinite matrices.