Robust Matrix Recovery through Nonconvex Optimization: Challenges and Promises



    Department of Systems Engineering and Engineering Management

                       The Chinese University of Hong Kong


Date: Monday, April 22, 4:30 pm – 5:30 pm

Venue: ERB 513, The Chinese University of Hong Kong

Title: Robust Matrix Recovery through Nonconvex Optimization: Challenges and Promises

Speaker: Mr. Jianhao Ma, University of Michigan



Robust matrix recovery is a foundational problem in modern
machine learning, with applications in motion detection, face
recognition, and collaborative filtering. In this talk, we explore
overparameterized robust matrix recovery, where the true rank is
unknown, and investigate its algorithmic and landscape properties.
Firstly, we uncover that the true solutions are saddle points, rather
than local or global minima of the objective function. Surprisingly,
we demonstrate that a simple subgradient method with small
initialization converges to the true solution, achieving nearly
optimal sample complexity. Our findings offer insights into the
emerging paradigm of robust machine learning and emphasize the need
for novel theories in nonsmooth optimization.


Jianhao Ma is currently a fourth-year Ph.D. student at the
Industrial and Operations Engineering Department of the University of
Michigan, Ann Arbor. His research lies broadly in robust machine
learning and nonconvex optimization. He received the Rackham
Predoctoral Fellowship from the University of Michigan. His papers
have won INFORMS JFIG Best Paper Award (second prize) and Katta Murty
Prize for Best Research Paper on Optimization (from IOE Department).

Everyone is welcome to attend the talk!

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Monday, April 22, 2024 - 16:30