Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Phase Transitions in Sparse PCA   We study optimal estimation for sparse principal component analysis when the
number of non-zero elements is small but on the same order as the dimension of
the data. We employ approximate message passing (AMP) algorithm and its state
evolution to analyze what is the information theoretically minimal mean-squared
error and the one achieved by AMP in the limit of large sizes. For a special
case of rank one and large enough density of non-zeros Deshpande and Montanari
[1] proved that AMP is asymptotically optimal. We show that both for low
density and for large rank the problem undergoes a series of phase transitions
suggesting existence of a region of parameters where estimation is information
theoretically possible, but AMP (and presumably every other polynomial
algorithm) fails. The analysis of the large rank limit is particularly
instructive.

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The categories of this paper are: funct-an
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The categories of this paper are: hep-ex
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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: q-bio
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The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: econ