[Colloquium] U of C - CS Theory Seminar - Haotian Jiang, October 1, 2024

[Jose J Fragoso via Colloquium]

UNIVERSITY OF CHICAGO
COMPUTER SCIENCE DEPARTMENT
PRESENTS



Haotian Jiang, PhD
Assistant Professor, University of Chicago


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Tuesday, October 1, 2024 at 3:30pm
Location: Kent 102

 Title: Tensor Concentration Inequalities: A Geometric Approach

Abstract: Matrix Concentration inequalities, commonly used in the forms of Matrix Chernoff Bounds or the Non-Commutative Khintchine Inequality, are central to a wide range of applications in computer science and mathematics. However, they fall short in many applications where tensor versions of these inequalities are required.

In this work, we study concentration inequalities for the $\ell_p$-injective norms of sums of independent tensors. We obtain the first such inequalities beyond Rudelson's classical work on rank-1 tensors, and our tensor concentration inequalities are tight in certain regimes of $p$ and the order of the tensors. Our results are obtained via a geometric argument based on estimating the covering numbers for the natural stochastic processes corresponding to tensor injective norms.

We also discuss applications and connections of our inequalities to various other problems, e.g. tensor PCA, locally-decodable codes, and natural models for random tensors and their tensor extensions.


 Bio: Haotian Jiang is an Assistant Professor of computer science. Previously, he was a Postdoctoral Researcher at Microsoft Research, Redmond. In December 2022, he obtained his PhD from the Paul G. Allen School of Computer Science & Engineering at the University of Washington under the supervision of Yin Tat Lee. He is broadly interested in theoretical computer science and applied mathematics. His primary area of expertise is the design and analysis of algorithms for continuous and discrete optimization problems, and algorithm design through the lens of discrepancy theory. His work on optimization has been recognized by a Best Student Paper Award in SODA 2021.





Host: Alexander Razborov






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