High-dimensional learning remains an outstanding task where empirical successes often coexist alongside mathematical and statistical curses.

In this talk, we will describe two vignettes of this tension that underscore the importance of distributional assumptions.

First, we will describe the role of invariance and symmetry priors in a non-parametric learning setup, by studying the gains in sample complexity brought by incorporating these priors into the learning model. Next, we will describe the role of data structure on the computational side, by studying computational-to-statistical gaps arising in the seemingly simple problem of learning a single neuron.

Joint work with Alberto Bietti and Luca Venturi (first part), and Min Jae Song and Ilias Zadik (second part).

Bio: Joan Bruna is an Associate Professor at Courant Institute, New York University (NYU), in the Department of Computer Science, Department of Mathematics (affiliated) and the Center for Data Science. He belongs to the CILVR group and to the Math and Data groups. He is also a scholar at the Center for Computational Mathematics, Flatiron Institute (part of the Simons Foundation). His research interests focus on the theoretical foundations of machine learning, high-dimensional statistics and applications of neural networks to computational sciences. For his research contributions, he has been awarded a Sloan Research Fellowship (2018), a NSF CAREER Award (2019), a best paper award at ICMLA (2018) and the IAA Outstanding Paper Award.