Seminari del Dipartimento di Matematica

Seminario del 2025

Alice Cortinovis

Randomized Schatten norm estimation

analisi numerica

Schatten norms extend familiar matrix norms such as the Frobenius, spectral, and nuclear norms, but their computation typically requires a full singular value decomposition and is therefore too expensive for large-scale matrices. I will discuss a randomized estimator for Schatten-2p norms, based on an approach by Kong and Valiant. The focus will be on improved variance bounds that provide a more accurate characterization of the estimator’s behavior for moderate sketch sizes and values of p, for matrices which are numerically low-rank. I will also compare the estimator with the Girard-Hutchinson's method, highlighting the trade-offs in terms of variance and matrix access. Numerical experiments illustrate how the theory reflects practice and indicate scenarios where these estimators are useful.