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An Assortment of Analyses of Optimal Transport Inspired by Domain Adaptation- [electronic resource]
An Assortment of Analyses of Optimal Transport Inspired by Domain Adaptation- [electronic resource]
상세정보
- 자료유형
- 학위논문파일 국외
- 최종처리일시
- 20240214095855
- ISBN
- 9798380618809
- DDC
- 310
- 저자명
- Pitcan, Yannik.
- 서명/저자
- An Assortment of Analyses of Optimal Transport Inspired by Domain Adaptation - [electronic resource]
- 발행사항
- [S.l.]: : University of California, Berkeley., 2021
- 발행사항
- Ann Arbor : : ProQuest Dissertations & Theses,, 2021
- 형태사항
- 1 online resource(96 p.)
- 주기사항
- Source: Dissertations Abstracts International, Volume: 85-04, Section: B.
- 주기사항
- Advisor: Bartlett, Peter.
- 학위논문주기
- Thesis (Ph.D.)--University of California, Berkeley, 2021.
- 사용제한주기
- This item must not be sold to any third party vendors.
- 초록/해제
- 요약This dissertation consists of several papers. First, we start off introducing domain adaptation theory and briefly introduce optimal transport. Such an introduction allows the reader to understand why studying problems in optimal transport theory is so valuable.Our first key result establishes bounds between regularized and unregularized optimal transport. Instead of using an entropic regularization, which is used in the Sinkhorn divergence, we regularize using dual potentials in a reproducing kernel Hilbert space. After this, we derive sample complexity bounds for the regularized optimal transport problem, and we show this is a substantial improvement over unregularized optimal transport. With these two results, one can approximate the theoretical optimal transport distance.Next, we prove the first and second moments of the source and target distributions are enough to determine explicitly the optimal transport map and also that this is a linear mapping. Furthermore, we propose an alternative regularization for the transport map between two distributions.After this, we briefly diverge from optimal transport theory and introduce work on prior elicitation. In particular, we extend a result from on non-asymptotic bounds for maximum likelihood estimators to that for M-estimators. Crucially, we show sufficient assumptions for these to hold and use these to theoretically justify our prior elicitation objective.Last, we return to optimal transport and introduce a variant to compare multiple probability measures, which we call sliced multi-marginal optimal transport. There, we propose a paradigm based on random one-dimensional projections.
- 일반주제명
- Statistics.
- 일반주제명
- Computer science.
- 일반주제명
- Mathematics.
- 기타저자
- University of California, Berkeley Statistics
- 기본자료저록
- Dissertations Abstracts International. 85-04B.
- 기본자료저록
- Dissertation Abstract International
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■00520240214095855
■006m o d
■007cr#unu||||||||
■020 ▼a9798380618809
■035 ▼a(MiAaPQ)AAI28718889
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a310
■1001 ▼aPitcan, Yannik.
■24513▼aAn Assortment of Analyses of Optimal Transport Inspired by Domain Adaptation▼h[electronic resource]
■260 ▼a[S.l.]:▼bUniversity of California, Berkeley. ▼c2021
■260 1▼aAnn Arbor :▼bProQuest Dissertations & Theses, ▼c2021
■300 ▼a1 online resource(96 p.)
■500 ▼aSource: Dissertations Abstracts International, Volume: 85-04, Section: B.
■500 ▼aAdvisor: Bartlett, Peter.
■5021 ▼aThesis (Ph.D.)--University of California, Berkeley, 2021.
■506 ▼aThis item must not be sold to any third party vendors.
■520 ▼aThis dissertation consists of several papers. First, we start off introducing domain adaptation theory and briefly introduce optimal transport. Such an introduction allows the reader to understand why studying problems in optimal transport theory is so valuable.Our first key result establishes bounds between regularized and unregularized optimal transport. Instead of using an entropic regularization, which is used in the Sinkhorn divergence, we regularize using dual potentials in a reproducing kernel Hilbert space. After this, we derive sample complexity bounds for the regularized optimal transport problem, and we show this is a substantial improvement over unregularized optimal transport. With these two results, one can approximate the theoretical optimal transport distance.Next, we prove the first and second moments of the source and target distributions are enough to determine explicitly the optimal transport map and also that this is a linear mapping. Furthermore, we propose an alternative regularization for the transport map between two distributions.After this, we briefly diverge from optimal transport theory and introduce work on prior elicitation. In particular, we extend a result from on non-asymptotic bounds for maximum likelihood estimators to that for M-estimators. Crucially, we show sufficient assumptions for these to hold and use these to theoretically justify our prior elicitation objective.Last, we return to optimal transport and introduce a variant to compare multiple probability measures, which we call sliced multi-marginal optimal transport. There, we propose a paradigm based on random one-dimensional projections.
■590 ▼aSchool code: 0028.
■650 4▼aStatistics.
■650 4▼aComputer science.
■650 4▼aMathematics.
■653 ▼aOptimal transport
■653 ▼aEntropic regularization
■653 ▼aSample complexity
■653 ▼aPrior elicitation
■653 ▼aDimensional projections
■690 ▼a0463
■690 ▼a0984
■690 ▼a0405
■71020▼aUniversity of California, Berkeley▼bStatistics.
■7730 ▼tDissertations Abstracts International▼g85-04B.
■773 ▼tDissertation Abstract International
■790 ▼a0028
■791 ▼aPh.D.
■792 ▼a2021
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T16931024▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
■980 ▼a202402▼f2024
