Source Identification for Mixtures of Product Distributions

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 $2^{O(k^2)}{n}^{O(k)}$ 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).

References in corpus (4)

• Identifiability of parameters in latent structure models with many observed variables
• Consistent Estimation of Identifiable Nonparametric Mixture Models from Grouped Observations
• On The Identifiability of Mixture Models from Grouped Samples
• On the Identifiability of Finite Mixtures of Finite Product Measures