자료유형  

 학위논문

Control Number  

0017160359

International Standard Book Number  

9798382781877

Dewey Decimal Classification Number  

310

Main Entry-Personal Name  

Qiu, Jiaze.

Publication, Distribution, etc. (Imprint  

[S.l.] : Harvard University., 2024

Publication, Distribution, etc. (Imprint  

Ann Arbor : ProQuest Dissertations & Theses, 2024

Physical Description  

184 p.

General Note  

Source: Dissertations Abstracts International, Volume: 85-12, Section: B.

General Note  

Advisor: Sen, Subhabrata.

Dissertation Note  

Thesis (Ph.D.)--Harvard University, 2024.

Summary, Etc.  

요약In modern applications of Bayesian Statistics, the posterior distribution is typically high-dimensional and analytically intractable. Variational Inference (VI) has emerged as an attractive option to approximate these intractable distributions, facilitating fast, parallel computations. The simplest version of VI is the Naive Mean-field approximation (NMF), where the distribution of interest is approximated by a product distribution. In recent years, another strategy rooted in statistical physics, the Thouless-Anderson-Palmer (TAP) formulation, started to garner increasing attention from theorists and practitioners alike. However, despite the rapidly growing popularity of variational approximations in Statistics and Machine Learning, the corresponding theoretical guarantees for these approximations remain largely unexplored. This dissertation addresses this challenge through three main contributions: TAP Approximation in Bayesian Linear Regression: In Chapter 1, a variational representation for the log-normalizing constant of the posterior distribution in Bayesian linear regression is derived in the proportional asymptotic regime, assuming a uniform spherical prior and i.i.d. Gaussian designs. Performance of NMF in Linear Regression: Chapter 2 investigates the NMF approximation in linear regression under proportional asymptotics. It confirms the inaccuracy of NMF for approximating the log-normalizing constant and supports empirical observations of NMF being overconfident. NMF in Generalized Linear Models (GLMs): Chapter 3 identifies conditions under which the NMF approximation is valid in high-dimensional GLMs. Algorithmic insights and probabilistic properties of the high-dimensional posteriors were also investigated.

Subject Added Entry-Topical Term  

Statistics.

Subject Added Entry-Topical Term  

Applied mathematics.

Subject Added Entry-Topical Term  

Statistical physics.

Index Term-Uncontrolled  

Variational inference

Index Term-Uncontrolled  

Thouless-Anderson-Palmer

Index Term-Uncontrolled  

Linear regression

Index Term-Uncontrolled  

Bayesian models

Index Term-Uncontrolled  

Gaussian designs

Added Entry-Corporate Name  

Harvard University Statistics

Host Item Entry  

Dissertations Abstracts International. 85-12B.

Electronic Location and Access  

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Control Number  

joongbu:654600