高维线性回归的TAP自由能

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-03-14 DOI:10.1214/22-aap1874

Jia Qiu, Subhabrata Sen

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引用次数: 6

摘要

我们推导了均匀球面先验和i.i.d高斯设计的贝叶斯线性回归中后验分布的对数归一化常数的变分表示。我们在“比例”渐近状态下工作，其中观测值的数量和特征的数量以比例速率增长。这严格地建立了自旋玻璃理论产生的thoulless - anderson - palmer (TAP)近似，并证明了Krzakala et. al.(2014)在球形先验的特殊情况下的一个猜想。

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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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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.