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 \eta where A is an unknown n \times n matrix and x is chosen uniformly at random from \{ 1, -1\} n, \eta is an n -dimensional Gaussian random variable with unknown covariance \Sigma: We give an algorithm that provable recovers A and \Sigma up to an additive \epsilon whose running time and sample complexity are polynomial in n and 1 / \epsilon . 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.

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 $y Ax \eta$ where $A$ is an unknown $n \times n$ matrix and $x$ is chosen uniformly at random from $\{ 1, -1\} n$, $\eta$ is an $n$-dimensional Gaussian random variable with unknown covariance $\Sigma$: We give an algorithm that provable recovers $A$ and $\Sigma$ up to an additive $\epsilon$ whose running time and sample complexity are polynomial in $n$ and $1 / \epsilon$. 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. Papers published at the Neural Information Processing Systems Conference.