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Stochastics and Statistics Seminar

On Provably Learning Sparse High-Dimensional Functions

March 8 @ 11:00 am - 12:00 pm

Joan Bruna, New York University

E18-304

Abstract: Neural Networks are hailed for their ability to discover useful low-dimensional ‘features’ out of complex high-dimensional data, yet such ability remains mostly hand-wavy. Over the recent years, the class of sparse (or ‘multi-index’) functions has emerged as a model with both practical motivations and a rich mathematical structure, enabling a quantitative theory of ‘feature learning’. In this talk, I will present recent progress on this front, by describing (i) the ability of gradient-descent algorithms to efficiently learn the multi-index class over Gaussian data, and (ii) the tight Statistical-Query complexity for the gaussian single-index class. 
Joint work with Loucas Pillaud-Vivien, Alex Damian, Alberto Bietti and Jason Lee.
 
Bio: Joan Bruna is an Associate Professor of Computer Science, Data Science and Mathematics (affiliated) at the Courant Institute and the Center for Data Science, New York University (NYU). He is also a visiting scholar at the Center for Computational Mathematics in the Flatiron Institute. His research interests are in the mathematical foundations of machine learning, including deep learning theory, and its interface with applied mathematics and problems in computational science. For his research contributions, he has been awarded a Sloan Research Fellowship, a NSF CAREER Award, and several best paper awards. 

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