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Variational Inference in High-dimensional Bayesian Regression Models.
Variational Inference in High-dimensional Bayesian Regression Models.
상세정보
- 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
- 로그인을 한후 보실 수 있는 자료입니다.
- Control Number
- joongbu:654600
MARC
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■0820 ▼a310
■1001 ▼aQiu, Jiaze.▼0(orcid)0000-0003-3895-1859
■24510▼aVariational Inference in High-dimensional Bayesian Regression Models.
■260 ▼a[S.l.]▼bHarvard University. ▼c2024
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2024
■300 ▼a184 p.
■500 ▼aSource: Dissertations Abstracts International, Volume: 85-12, Section: B.
■500 ▼aAdvisor: Sen, Subhabrata.
■5021 ▼aThesis (Ph.D.)--Harvard University, 2024.
■520 ▼aIn 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.
■590 ▼aSchool code: 0084.
■650 4▼aStatistics.
■650 4▼aApplied mathematics.
■650 4▼aStatistical physics.
■653 ▼aVariational inference
■653 ▼aThouless-Anderson-Palmer
■653 ▼aLinear regression
■653 ▼aBayesian models
■653 ▼aGaussian designs
■690 ▼a0463
■690 ▼a0364
■690 ▼a0217
■71020▼aHarvard University▼bStatistics.
■7730 ▼tDissertations Abstracts International▼g85-12B.
■790 ▼a0084
■791 ▼aPh.D.
■792 ▼a2024
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17160359▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
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