高维线性回归的TAP自由能

IF 1.4 2区数学 Q2 STATISTICS & PROBABILITY

Annals of Applied Probability 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

Annals of Applied Probability 数学-统计学与概率论

CiteScore

2.70

自引率

5.60%

发文量

108

审稿时长

6-12 weeks

期刊介绍： The Annals of Applied Probability aims to publish research of the highest quality reflecting the varied facets of contemporary Applied Probability. Primary emphasis is placed on importance and originality.