Provable ICA with unknown Gaussian noise, with implications for Gaussian mixtures and autoencoders

Journal Article

We present a new algorithm for Independent Component Analysis (ICA) which has provable performance guarantees. In particular, suppose we are given samples of the form y = Ax +η where A is an unknown n × n matrix and x is a random variable whose components are independent and have a fourth moment strictly less than that of a standard Gaussian random variable and η is an n-dimensional Gaussian random variable with unknown covariance ∑ We give an algorithm that provable recovers A and ∑ up to an additive ε and whose running time and sample complexity are polynomial in n and 1/ε To accomplish this, we introduce a novel "quasi-whitening" step that may be useful in other contexts in which the covariance of Gaussian noise is not known in advance. We also give a general framework for finding all local optima of a function (given an oracle for approximately finding just one) and this is a crucial step in our algorithm, one that has been overlooked in previous attempts, and allows us to control the accumulation of error when we find the columns of A one by one via local search.

Duke Authors

Cited Authors

  • Arora, S; Ge, R; Moitra, A; Sachdeva, S

Published Date

  • December 1, 2012

Published In

Volume / Issue

  • 3 /

Start / End Page

  • 2375 - 2383

International Standard Serial Number (ISSN)

  • 1049-5258

Citation Source

  • Scopus