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Advances in Amortized Bayesian Inference, with Applications to Astronomy
Advances in Amortized Bayesian Inference, with Applications to Astronomy
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20260202105238
- ISBN
- 9798291568095
- DDC
- 310
- 서명/저자
- Advances in Amortized Bayesian Inference, with Applications to Astronomy
- 발행사항
- [Sl] : University of Michigan, 2025
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2025
- 형태사항
- 182 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 87-02, Section: B.
- 주기사항
- Advisor: Regier, Jeffrey.
- 학위논문주기
- Thesis (Ph.D.)--University of Michigan, 2025.
- 초록/해제
- 요약Approximate Bayesian methods provide a principled means for inference in settings in which exact posterior inference is intractable. In this work, I present methods for variational inference, an approach to approximate Bayesian inference in which an approximation to the posterior is selected by numerical optimization. The approaches and analysis primarily consider amortized variational inference, a class of techniques that leverages deep learning to obtain a mapping from data instances to variational approximations of the posterior. First, I present SMC-Wake, a likelihood-based approach for minimization of the forward KL divergence. This algorithm uses Sequential Monte Carlo (SMC) samplers to construct inexpensive particle approximations for training an inference network. Next, I present a study of neural posterior estimation (NPE) and its objective function, the expected forward KL divergence. This likelihood-free approach to amortized inference averages over large amounts of simulated data from the model to learn mappings from data instances to variational approximations of the posterior. I present an analysis of this approach from the perspective of neural tangent kernel (NTK) theory. Under certain conditions on the variational family and neural network mapping, I show that NPE optimizes a convex functional and reliably converges to a unique solution in the asymptotic infinite-width limit, despite the highly nonconvex nature of neural network optimization landscapes. Finally, I extend these results to posit a novel class of expressive variational families based on linear combinations of basis functions, and propose a procedure to adaptively fit these basis functions to parameterize complex distributions. When targeting the forward KL divergence within this framework, the objective is convex in the variational parameters, but nevertheless allows for practitioners to fit highly multimodal variational approximations to the posterior. We conclude with applications of these methods to difficult problems in astronomy, such as redshift estimation from astronomical images, and the task of detecting blended astronomical spectra.
- 일반주제명
- Statistics
- 일반주제명
- Astronomy
- 일반주제명
- Computational physics
- 기타저자
- University of Michigan Statistics
- 기본자료저록
- Dissertations Abstracts International. 87-02B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■00520260202105238
■006m o d
■007cr#unu||||||||
■020 ▼a9798291568095
■035 ▼a(MiAaPQ)AAI32271975
■035 ▼a(MiAaPQ)umichrackham006265
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a310
■1001 ▼aMcNamara, Declan Matthias.
■24510▼aAdvances in Amortized Bayesian Inference, with Applications to Astronomy
■260 ▼a[Sl]▼bUniversity of Michigan▼c2025
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2025
■300 ▼a182 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 87-02, Section: B.
■500 ▼aAdvisor: Regier, Jeffrey.
■5021 ▼aThesis (Ph.D.)--University of Michigan, 2025.
■520 ▼aApproximate Bayesian methods provide a principled means for inference in settings in which exact posterior inference is intractable. In this work, I present methods for variational inference, an approach to approximate Bayesian inference in which an approximation to the posterior is selected by numerical optimization. The approaches and analysis primarily consider amortized variational inference, a class of techniques that leverages deep learning to obtain a mapping from data instances to variational approximations of the posterior. First, I present SMC-Wake, a likelihood-based approach for minimization of the forward KL divergence. This algorithm uses Sequential Monte Carlo (SMC) samplers to construct inexpensive particle approximations for training an inference network. Next, I present a study of neural posterior estimation (NPE) and its objective function, the expected forward KL divergence. This likelihood-free approach to amortized inference averages over large amounts of simulated data from the model to learn mappings from data instances to variational approximations of the posterior. I present an analysis of this approach from the perspective of neural tangent kernel (NTK) theory. Under certain conditions on the variational family and neural network mapping, I show that NPE optimizes a convex functional and reliably converges to a unique solution in the asymptotic infinite-width limit, despite the highly nonconvex nature of neural network optimization landscapes. Finally, I extend these results to posit a novel class of expressive variational families based on linear combinations of basis functions, and propose a procedure to adaptively fit these basis functions to parameterize complex distributions. When targeting the forward KL divergence within this framework, the objective is convex in the variational parameters, but nevertheless allows for practitioners to fit highly multimodal variational approximations to the posterior. We conclude with applications of these methods to difficult problems in astronomy, such as redshift estimation from astronomical images, and the task of detecting blended astronomical spectra.
■590 ▼aSchool code: 0127.
■650 4▼aStatistics
■650 4▼aAstronomy
■650 4▼aComputational physics
■653 ▼aVariational inference
■653 ▼aNeural posterior estimation
■653 ▼aSimulation-based inference
■653 ▼aSequential Monte Carlo
■653 ▼aNeural tangent kernel theory
■690 ▼a0463
■690 ▼a0800
■690 ▼a0216
■690 ▼a0606
■71020▼aUniversity of Michigan▼bStatistics.
■7730 ▼tDissertations Abstracts International▼g87-02B.
■790 ▼a0127
■791 ▼aPh.D.
■792 ▼a2025
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17359938▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
