Introducing Discrepancy Values of Matrices and Their Applications

Wednesday, December 15, 2021 - 4:00pm to 4:30pm

Event Calendar Category

LIDS & Stats Tea

Speaker Name

Poorya Habibzadeh

Affiliation

LIDS & IDSS

Building and Room Number

LIDS Lounge

Abstract

We introduce discrepancy values, quantities that are inspired by the notion of spectral spread of Hermitian matrices. In particular, the discrepancy values capture the difference between two consecutive (Ky-Fan-like) pseudo-norms that we also introduce. As a result, discrepancy values share many properties with singular values and eigenvalues, and yet are substantially different to merit their own study. We describe several key properties of discrepancy values and establish a set of useful tools (e.g., representation theorems, majorization inequalities, convex optimization formulations, etc.) for working with them. As an important application, we illustrate the role of discrepancy values in deriving tight bounds on the norms of commutators.

The preprint of our article can be found at: https://arxiv.org/abs/2111.11855

Biography

Pourya Habib Zadeh is a third year PhD student at MIT, EECS department, advised by Professor Suvrit Sra. He obtained his M.S. from university of Tehran at 2016. Pourya's research focuses on Matrix theory, machine learning and optimization.