Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Provable ICA with Unknown Gaussian Noise, and Implications for Gaussian
  Mixtures and Autoencoders   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.

12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph