Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The TAP free energy for high-dimensional linear regression   We derive a variational representation for the log-normalizing constant of
the posterior distribution in Bayesian linear regression with a uniform
spherical prior and an i.i.d. Gaussian design. We work under the "proportional"
asymptotic regime, where the number of observations and the number of features
grow at a proportional rate. This rigorously establishes the
Thouless-Anderson-Palmer (TAP) approximation arising from spin glass theory,
and proves a conjecture of Krzakala et. al. (2014) in the special case of the
spherical prior.

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The categories of this paper are: dg-ga
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The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
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The categories of this paper are: nlin
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The categories of this paper are: funct-an
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The categories of this paper are: astro-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: cond-mat