The Probabilitas Seminar series focuses on high-dimensional problems that combine statistics, probability, artificial intelligence, information theory, computer science, and other related fields. The upcoming seminar takes place on Tuesday, October 28, at 1:30pm in Science Center 705. This week's speaker will be Alex Damian, research fellow at the Harvard Kempner Institute.
Learning From Gaussian Data: Single and Multi-Index Models
Abstract: In this work we consider generic Gaussian Multi-index models, in which the labels only depend on the (Gaussian) d-dimensional inputs through their projection onto a low-dimensional subspace, and we study efficient agnostic estimation procedures for this hidden subspace. We introduce the generative leap exponent k*, a natural extension of the generative exponent from [DPVLB24] to the multi-index setting. We first show that a sample complexity of n= Θ(d^{1∨k*/2}) is necessary in the class of algorithms captured by the Low-Degree-Polynomial framework. We then establish that this sample complexity is also sufficient, by giving an agnostic sequential estimation procedure (that is, requiring no prior knowledge of the multi-index model) based on a spectral U-statistic over appropriate Hermite tensors. We further compute the generative leap exponent for several examples including piecewise linear functions (deep ReLU networks with bias).
Topic: Alex Damian seminar
Time: Oct 28, 2025 01:30 PM Eastern Time (US and Canada)
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Meeting ID: 990 5600 3111
LOCATION:Science Center 705 STATUS:CONFIRMED DTSTART:20251028T173000Z DTEND:20251028T183000Z END:VEVENT END:VCALENDAR