[Theory] UC Theory Seminar

[Alexander Razborov via Theory]

Haotian Jiang, PhD
Assistant Professor, University of Chicago
 
 

 
 
Tuesday, October 1, 2024 at 3:30pm
Location: TBD
 
 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. 
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