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Rare-Event Analysis for Heavy-Tailed Systems With Applications in Statistical Learning and Simulation
Rare-Event Analysis for Heavy-Tailed Systems With Applications in Statistical Learning and Simulation
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20250211152131
- ISBN
- 9798384015819
- DDC
- 658
- 저자명
- Wang, Xingyu.
- 서명/저자
- Rare-Event Analysis for Heavy-Tailed Systems With Applications in Statistical Learning and Simulation
- 발행사항
- [Sl] : Northwestern University, 2024
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2024
- 형태사항
- 309 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 86-02, Section: A.
- 주기사항
- Advisor: Rhee, Chang-Han.
- 학위논문주기
- Thesis (Ph.D.)--Northwestern University, 2024.
- 초록/해제
- 요약Heavy-tailed phenomena arise naturally in a variety of stochastic systems in fields such as mathematical finance, operations research, and machine learning, capturing the extreme variability where large shocks occur more often than typically expected. This dissertation develops a theoretical framework for rare-event analysis in heavy-tailed systems and provides applications in statistical learning and simulation. Specifically, we focus on the power-law (i.e., regularly varying) type of heavy tails and develop a framework that connects large deviations and metastability analysis for heavy-tailed dynamical systems. The results characterize the catastrophe principle that reveals a discrete hierarchy governing the causes and probabilities of a wide variety of rare events associated with heavy-tailed stochastic difference/differential equations, and unveil an intriguing phase transition in the local stability of stochastic dynamics under truncated heavy tails. Building upon this framework, we then provide a sharp characterization of the global dynamics of heavy-tailed stochastic gradient descents. In the context of deep learning, our results lead to a tail-inflation-and-truncation training strategy that improves the generalization performance of deep neural nets. Additionally, we propose a highly efficient rare-event simulation algorithm for heavy-tailed systems and address the computationally challenging cases where the underlying process exhibits infinite activities. In the last chapter, we discuss future research directions.
- 일반주제명
- Industrial engineering
- 일반주제명
- Applied mathematics
- 기타저자
- Northwestern University Industrial Engineering and Management Sciences
- 기본자료저록
- Dissertations Abstracts International. 86-02A.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■020 ▼a9798384015819
■035 ▼a(MiAaPQ)AAI31483324
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a658
■1001 ▼aWang, Xingyu.
■24510▼aRare-Event Analysis for Heavy-Tailed Systems With Applications in Statistical Learning and Simulation
■260 ▼a[Sl]▼bNorthwestern University▼c2024
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2024
■300 ▼a309 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 86-02, Section: A.
■500 ▼aAdvisor: Rhee, Chang-Han.
■5021 ▼aThesis (Ph.D.)--Northwestern University, 2024.
■520 ▼aHeavy-tailed phenomena arise naturally in a variety of stochastic systems in fields such as mathematical finance, operations research, and machine learning, capturing the extreme variability where large shocks occur more often than typically expected. This dissertation develops a theoretical framework for rare-event analysis in heavy-tailed systems and provides applications in statistical learning and simulation. Specifically, we focus on the power-law (i.e., regularly varying) type of heavy tails and develop a framework that connects large deviations and metastability analysis for heavy-tailed dynamical systems. The results characterize the catastrophe principle that reveals a discrete hierarchy governing the causes and probabilities of a wide variety of rare events associated with heavy-tailed stochastic difference/differential equations, and unveil an intriguing phase transition in the local stability of stochastic dynamics under truncated heavy tails. Building upon this framework, we then provide a sharp characterization of the global dynamics of heavy-tailed stochastic gradient descents. In the context of deep learning, our results lead to a tail-inflation-and-truncation training strategy that improves the generalization performance of deep neural nets. Additionally, we propose a highly efficient rare-event simulation algorithm for heavy-tailed systems and address the computationally challenging cases where the underlying process exhibits infinite activities. In the last chapter, we discuss future research directions.
■590 ▼aSchool code: 0163.
■650 4▼aIndustrial engineering
■650 4▼aApplied mathematics
■653 ▼aMathematical finance
■653 ▼aHeavy-tailed systems
■653 ▼aStochastic systems
■653 ▼aRare-event analysis
■690 ▼a0546
■690 ▼a0364
■690 ▼a0796
■690 ▼a0454
■71020▼aNorthwestern University▼bIndustrial Engineering and Management Sciences.
■7730 ▼tDissertations Abstracts International▼g86-02A.
■790 ▼a0163
■791 ▼aPh.D.
■792 ▼a2024
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17163070▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
