서브메뉴
검색
Learning Low-Dimensional Structures in High Dimensions
Learning Low-Dimensional Structures in High Dimensions
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20260202103113
- ISBN
- 9798280720138
- DDC
- 310
- 저자명
- Song, Yanke.
- 서명/저자
- Learning Low-Dimensional Structures in High Dimensions
- 발행사항
- [Sl] : Harvard University, 2025
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2025
- 형태사항
- 295 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 86-12, Section: B.
- 주기사항
- Advisor: Sur, Pragya.
- 학위논문주기
- Thesis (Ph.D.)--Harvard University, 2025.
- 초록/해제
- 요약Although researchers nowadays deal with increasingly high-dimensional datasets, lower-dimensional structures often exist and learning them effectively play a crucial role. This dissertation contributes to this effort by developing theories and methodologies for learning low dimensional structures in high dimensions, developed by the author and collaborators. The first two chapters focus on learning one-dimensional functionals in the proportional asymptotics setting, where the number of observations grows proportionally with the number of features. The theories developed in this asymptotic regime reveals surprising new phenomena and exhibit remarkable accuracy in finite samples of high dimensions, where classical theories fail. Chapter 1 investigates heritability estimation under this framework. We study the joint distribution of debiased Lasso and Ridge estimators under proportional asymptotics, and consequently propose a heritability estimator that features an adaptive tuning procedure. Empirical studies confirm its efficiency and robustness compared to previous methods. Chapter 2 focus on transfer learning in linear models. Within proportional asymptotics framework, we precisely characterize the generalization error of minnorm interpolators under both design and model shifts, and confirm the finite sample accuracy via simulations. This analysis identifies regimes where transfer learning is beneficial, and provides relevant guidelines for practitioners. Chapter 3 shifts focus to unsupervised learning of high-dimensional Poisson process arrival data. We propose an end-to-end pipeline that not only reconstructs underlying (inhomogeneous) rate functions of Poisson processes, but also learns low-dimensional representations that are valuable for downstream learning tasks.
- 일반주제명
- Statistics
- 일반주제명
- Applied mathematics
- 일반주제명
- Computer science
- 기타저자
- Harvard University Statistics
- 기본자료저록
- Dissertations Abstracts International. 86-12B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
008260126s2025 us c eng d■001000017356990
■00520260202103113
■006m o d
■007cr#unu||||||||
■020 ▼a9798280720138
■035 ▼a(MiAaPQ)AAI31936464
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a310
■1001 ▼aSong, Yanke.▼0(orcid)0009-0008-6173-6931
■24510▼aLearning Low-Dimensional Structures in High Dimensions
■260 ▼a[Sl]▼bHarvard University▼c2025
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2025
■300 ▼a295 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 86-12, Section: B.
■500 ▼aAdvisor: Sur, Pragya.
■5021 ▼aThesis (Ph.D.)--Harvard University, 2025.
■520 ▼aAlthough researchers nowadays deal with increasingly high-dimensional datasets, lower-dimensional structures often exist and learning them effectively play a crucial role. This dissertation contributes to this effort by developing theories and methodologies for learning low dimensional structures in high dimensions, developed by the author and collaborators. The first two chapters focus on learning one-dimensional functionals in the proportional asymptotics setting, where the number of observations grows proportionally with the number of features. The theories developed in this asymptotic regime reveals surprising new phenomena and exhibit remarkable accuracy in finite samples of high dimensions, where classical theories fail. Chapter 1 investigates heritability estimation under this framework. We study the joint distribution of debiased Lasso and Ridge estimators under proportional asymptotics, and consequently propose a heritability estimator that features an adaptive tuning procedure. Empirical studies confirm its efficiency and robustness compared to previous methods. Chapter 2 focus on transfer learning in linear models. Within proportional asymptotics framework, we precisely characterize the generalization error of minnorm interpolators under both design and model shifts, and confirm the finite sample accuracy via simulations. This analysis identifies regimes where transfer learning is beneficial, and provides relevant guidelines for practitioners. Chapter 3 shifts focus to unsupervised learning of high-dimensional Poisson process arrival data. We propose an end-to-end pipeline that not only reconstructs underlying (inhomogeneous) rate functions of Poisson processes, but also learns low-dimensional representations that are valuable for downstream learning tasks.
■590 ▼aSchool code: 0084.
■650 4▼aStatistics
■650 4▼aApplied mathematics
■650 4▼aComputer science
■653 ▼aHigh-dimensional statistics
■653 ▼aPoisson processes
■653 ▼aSignal-to-noise ratio
■653 ▼aTransfer learning
■653 ▼aDownstream learning
■690 ▼a0463
■690 ▼a0984
■690 ▼a0364
■71020▼aHarvard University▼bStatistics.
■7730 ▼tDissertations Abstracts International▼g86-12B.
■790 ▼a0084
■791 ▼aPh.D.
■792 ▼a2025
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17356990▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
