Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bilinear Generalized Vector Approximate Message Passing   We introduce the bilinear generalized vector approximate message passing
(BiG-VAMP) algorithm which jointly recovers two matrices U and V from their
noisy product through a probabilistic observation model. BiG-VAMP provides
computationally efficient approximate implementations of both max-sum and
sumproduct loopy belief propagation (BP). We show how the proposed BiG-VAMP
algorithm recovers different types of structured matrices and overcomes the
fundamental limitations of other state-of-the-art approaches to the bilinear
recovery problem, such as BiG-AMP, BAd-VAMP and LowRAMP. In essence, BiG-VAMP
applies to a broader class of practical applications which involve a general
form of structured matrices. For the sake of theoretical performance
prediction, we also conduct a state evolution (SE) analysis of the proposed
algorithm and show its consistency with the asymptotic empirical mean-squared
error (MSE). Numerical results on various applications such as matrix
factorization, dictionary learning, and matrix completion demonstrate
unambiguously the effectiveness of the proposed BiG-VAMP algorithm and its
superiority over stateof-the-art algorithms. Using the developed SE framework,
we also examine (as one example) the phase transition diagrams of the matrix
completion problem, thereby unveiling a low detectability region corresponding
to the low signal-to-noise ratio (SNR) regime.

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The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat