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Algorithm Dynamics in Modern Statistical Learning: Asymptotics, Universality, and Implicit Regularization
Algorithm Dynamics in Modern Statistical Learning: Asymptotics, Universality, and Implicit Regularization
Detailed Information
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20250211151036
- ISBN
- 9798383482179
- DDC
- 310
- 저자명
- Wang, Tianhao.
- 서명/저자
- Algorithm Dynamics in Modern Statistical Learning: Asymptotics, Universality, and Implicit Regularization
- 발행사항
- [Sl] : Yale University, 2024
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2024
- 형태사항
- 349 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 86-01, Section: B.
- 주기사항
- Advisor: Fan, Zhou.
- 학위논문주기
- Thesis (Ph.D.)--Yale University, 2024.
- 초록/해제
- 요약Understanding the dynamics of algorithms is crucial for characterizing the behavior of trained models in modern statistical learning. This thesis presents a few recent results on theoretical analyses of the dynamics of two classes of algorithms: Approximate Message Passing (AMP) algorithms and Stochastic Gradient Descent (SGD). For AMP algorithms, the focus is to derive the precise asymptotic distributional characterization of the iterates, known as the ``state evolution'' which summarizes the dynamics of AMP iterates, and to understand the universality of such characterization with respect to the underlying data distribution. For SGD, the goal is to perform trajectory analysis to understand its implicit regularization, a key property believed to be essential for the generalization of modern deep learning models. The results presented here provide unified frameworks for analyzing and understanding the dynamics of these algorithms, and can be potentially extended to other algorithms.
- 일반주제명
- Statistics
- 키워드
- Universality
- 기타저자
- Yale University Statistics and Data Science
- 기본자료저록
- Dissertations Abstracts International. 86-01B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■035 ▼a(MiAaPQ)AAI30997623
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a310
■1001 ▼aWang, Tianhao.
■24510▼aAlgorithm Dynamics in Modern Statistical Learning: Asymptotics, Universality, and Implicit Regularization
■260 ▼a[Sl]▼bYale University▼c2024
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2024
■300 ▼a349 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 86-01, Section: B.
■500 ▼aAdvisor: Fan, Zhou.
■5021 ▼aThesis (Ph.D.)--Yale University, 2024.
■520 ▼aUnderstanding the dynamics of algorithms is crucial for characterizing the behavior of trained models in modern statistical learning. This thesis presents a few recent results on theoretical analyses of the dynamics of two classes of algorithms: Approximate Message Passing (AMP) algorithms and Stochastic Gradient Descent (SGD). For AMP algorithms, the focus is to derive the precise asymptotic distributional characterization of the iterates, known as the ``state evolution'' which summarizes the dynamics of AMP iterates, and to understand the universality of such characterization with respect to the underlying data distribution. For SGD, the goal is to perform trajectory analysis to understand its implicit regularization, a key property believed to be essential for the generalization of modern deep learning models. The results presented here provide unified frameworks for analyzing and understanding the dynamics of these algorithms, and can be potentially extended to other algorithms.
■590 ▼aSchool code: 0265.
■650 4▼aStatistics
■653 ▼aApproximate message passing
■653 ▼aImplicit regularization
■653 ▼aStochastic gradient descent
■653 ▼aUniversality
■690 ▼a0463
■71020▼aYale University▼bStatistics and Data Science.
■7730 ▼tDissertations Abstracts International▼g86-01B.
■790 ▼a0265
■791 ▼aPh.D.
■792 ▼a2024
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17160537▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
