Provable ICA with Unknown Gaussian Noise, with Implications for Gaussian Mixtures and Autoencoders

Sanjeev AroraRong GeAnkur MoitraSushant Sachdeva

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 $1 / \epsilon$... (read more)

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