TY - GEN
T1 - Provable ICA with unknown Gaussian noise, with implications for Gaussian mixtures and autoencoders
AU - Arora, Sanjeev
AU - Ge, Rong
AU - Moitra, Ankur
AU - Sachdeva, Sushant
PY - 2012
Y1 - 2012
N2 - 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.
AB - 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.
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M3 - Conference contribution
AN - SCOPUS:84877781888
SN - 9781627480031
T3 - Advances in Neural Information Processing Systems
SP - 2375
EP - 2383
BT - Advances in Neural Information Processing Systems 25
T2 - 26th Annual Conference on Neural Information Processing Systems 2012, NIPS 2012
Y2 - 3 December 2012 through 6 December 2012
ER -