[Theory] TODAY: [TTIC Talks] 11/7 Talks at TTIC: Khashayar Gatmiry, MIT

[Brandie Jones via Theory]

*When:*         Thursday, November 7th at* 12:30pm CT  *


*Where:*       Talk will be given *live, in-person* at

                       TTIC, 6045 S. Kenwood Avenue

                       5th Floor, Room 530


*Virtually:*     via Panopto (Livestream
<https://uchicago.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=93454137-39b1-4854-8990-b21b0119f973>
)


*Who:          *Khashayar Gatmiry, MIT


*Title:*           Learning Mixtures of Gaussians Using Diffusion Models


*Abstract:*  We give a new algorithm for learning mixtures of k Gaussians
(with identity covariance in R^n) to TV error ε, with quasi-polynomial
(O(n^{poly log((n+k)/ε)})) time and sample complexity, under a minimum
weight assumption. Unlike previous approaches, most of which are algebraic
in nature, our approach is analytic and relies on the framework of
diffusion models. Diffusion models are a modern paradigm for generative
modeling, which typically rely on learning the score function (gradient
log-pdf) along a process transforming a pure noise distribution, in our
case a Gaussian, to the data distribution. Despite their dazzling
performance in tasks such as image generation, there are few end-to-end
theoretical guarantees that they can efficiently learn nontrivial families
of distributions; we give some of the first such guarantees. We proceed by
deriving higher-order Gaussian noise sensitivity bounds for the score
functions for a Gaussian mixture to show that that they can be inductively
learned using piecewise polynomial regression (up to poly-logarithmic
degree), and combine this with known convergence results for diffusion
models. Our results extend to continuous mixtures of Gaussians where the
mixing distribution is supported on a union of k balls of constant radius.
In particular, this applies to the case of Gaussian convolutions of
distributions on low-dimensional manifolds, or more generally sets with
small covering number.

I will talk about our recent work on diffusion models in this link:
https://arxiv.org/abs/2404.18869

*Host: Zhiyuan Li <zhiyuanli at ttic.edu>*

-- 
*Brandie Jones *
*Executive **Administrative Assistant*
Toyota Technological Institute
6045 S. Kenwood Avenue
Chicago, IL  60637
www.ttic.edu
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