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• W2953204889 abstract "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 a random variable whose components are independent and have a fourth moment strictly less than that of a standard Gaussian random variable and $eta$ 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 $epsilon$ and 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." @default.
• W2953204889 created "2019-06-27" @default.
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• W2953204889 date "2012-06-23" @default.
• W2953204889 modified "2023-10-01" @default.
• W2953204889 title "Provable ICA with Unknown Gaussian Noise, and Implications for Gaussian Mixtures and Autoencoders" @default.
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