Robustly Learning General Mixtures of Gaussians

Autor:	Allen Liu, Ankur Moitra
Rok vydání:	2023
Předmět:	Artificial Intelligence Hardware and Architecture Control and Systems Engineering Software Information Systems
Zdroj:	Journal of the ACM. 70:1-53
ISSN:	1557-735X 0004-5411
Popis:	This work represents a natural coalescence of two important lines of work — learning mixtures of Gaussians and algorithmic robust statistics. In particular, we give the first provably robust algorithm for learning mixtures of any constant number of Gaussians. We require only mild assumptions on the mixing weights and that the total variation distance between components is bounded away from zero. At the heart of our algorithm is a new method for proving a type of dimension-independent polynomial identifiability — which we call robust identifiability — through applying a carefully chosen sequence of differential operations to certain generating functions that not only encode the parameters we would like to learn but also the system of polynomial equations we would like to solve. We show how the symbolic identities we derive can be directly used to analyze a natural sum-of-squares relaxation.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::e0a587ea69a35030310264a7468d663f https://doi.org/10.1145/3583680 Zobrazit plný text záznamu Plný text ve formátu PDF