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Non-convex Matrix Sensing: Breaking the Quadratic Rank Barrier in Sample Complexity

USC Probability and Statistics Seminar via YouTube

Overview

Learn about groundbreaking research in matrix reconstruction through this USC Probability and Statistics seminar talk that explores efficient methods for reconstructing low-rank matrices from limited linear measurements. Dive into the comparison between traditional convex approaches using nuclear norm minimization and computationally less expensive non-convex methods employing factorized gradient descent. Discover how the speaker improves upon existing techniques by reducing the sample complexity of non-convex matrix factorization from quadratic to linear rank-dependence when reconstructing positive semidefinite matrices from Gaussian measurements. Follow along as the presentation introduces a novel probabilistic decoupling argument demonstrating that gradient descent iterates maintain only weak dependencies on individual measurement matrix entries. The research, conducted in collaboration with Dominik Stöger from KU Eichstätt-Ingolstadt, represents a significant advancement in matrix sensing theory and computational efficiency.

Syllabus

Yizhe Zhu: Non-convex matrix sensing: Breaking the quadratic rank barrier in the sample com... (USC)

Taught by

USC Probability and Statistics Seminar

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