Alice Cortinovis

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.