Source Identification for Mixtures of Product Distributions

Spencer L. Gordon, Bijan Mazaheri, Yuval Rabani, Leonard J. Schulman

Research output: Contribution to journalConference articlepeer-review

8 Scopus citations

Abstract

We give an algorithm for source identification of a mixture of k product distributions on n bits. This is a fundamental problem in machine learning with many applications. Our algorithm identifies the source parameters of an identifiable mixture, given, as input, approximate values of multilinear moments (derived, for instance, from a sufficiently large sample), using 2O(k2)nO(k) arithmetic operations. Our result is the first explicit bound on the computational complexity of source identification of such mixtures. The running time improves previous results by Feldman, O’Donnell, and Servedio (FOCS 2005) and Chen and Moitra (STOC 2019) that guaranteed only learning the mixture (without parametric identification of the source). Our analysis gives a quantitative version of a qualitative characterization of identifiable sources that is due to Tahmasebi, Motahari, and Maddah-Ali (ISIT 2018).

Original languageAmerican English
Pages (from-to)2193-2216
Number of pages24
JournalProceedings of Machine Learning Research
Volume134
StatePublished - 2021
Event34th Conference on Learning Theory, COLT 2021 - Boulder, United States
Duration: 15 Aug 202119 Aug 2021

Bibliographical note

Funding Information:
Research supported in part by NSFC-ISF grant 2553-17, NSF-BSF grant 2018687, and NSF grants CCF-1618795 and 1909972. Part of this work was done while the third author visited Caltech. Thanks to anonymous reviewers for helpful comments.

Publisher Copyright:
© 2021 S.L. Gordon, B. Mazaheri, Y. Rabani & L.J. Schulman.

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