Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Convergence of Approximate Message Passing with Arbitrary
  Matrices   Approximate message passing (AMP) methods and their variants have attracted
considerable recent attention for the problem of estimating a random vector
$\mathbf{x}$ observed through a linear transform $\mathbf{A}$. In the case of
large i.i.d. zero-mean Gaussian $\mathbf{A}$, the methods exhibit fast
convergence with precise analytic characterizations on the algorithm behavior.
However, the convergence of AMP under general transforms $\mathbf{A}$ is not
fully understood. In this paper, we provide sufficient conditions for the
convergence of a damped version of the generalized AMP (GAMP) algorithm in the
case of quadratic cost functions (i.e., Gaussian likelihood and prior). It is
shown that, with sufficient damping, the algorithm is guaranteed to converge,
although the amount of damping grows with peak-to-average ratio of the squared
singular values of the transforms $\mathbf{A}$. This result explains the good
performance of AMP on i.i.d. Gaussian transforms $\mathbf{A}$, but also their
difficulties with ill-conditioned or non-zero-mean transforms $\mathbf{A}$. A
related sufficient condition is then derived for the local stability of the
damped GAMP method under general cost functions, assuming certain strict
convexity conditions.

18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
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The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th