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Variational Inference in High-dimensional Bayesian Regression Models
Variational Inference in High-dimensional Bayesian Regression Models
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20250211151004
- ISBN
- 9798382781877
- DDC
- 310
- 저자명
- Qiu, Jiaze.
- 서명/저자
- Variational Inference in High-dimensional Bayesian Regression Models
- 발행사항
- [Sl] : Harvard University, 2024
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2024
- 형태사항
- 184 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 85-12, Section: B.
- 주기사항
- Advisor: Sen, Subhabrata.
- 학위논문주기
- Thesis (Ph.D.)--Harvard University, 2024.
- 초록/해제
- 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.
- 일반주제명
- Statistics
- 일반주제명
- Applied mathematics
- 일반주제명
- Statistical physics
- 키워드
- Bayesian models
- 키워드
- Gaussian designs
- 기타저자
- Harvard University Statistics
- 기본자료저록
- Dissertations Abstracts International. 85-12B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■020 ▼a9798382781877
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■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a310
■1001 ▼aQiu, Jiaze.▼0(orcid)0000-0003-3895-1859
■24510▼aVariational Inference in High-dimensional Bayesian Regression Models
■260 ▼a[Sl]▼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.
