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Statistical Learning and Optimal Decision Making Under Uncertainty- [electronic resource]
![Statistical Learning and Optimal Decision Making Under Uncertainty - [electronic resource]](/Users/Baul/Images/book.png)
Statistical Learning and Optimal Decision Making Under Uncertainty- [electronic resource]
상세정보
- 자료유형
- 학위논문파일 국외
- 최종처리일시
- 20240214101246
- ISBN
- 9798380413930
- DDC
- 310
- 저자명
- Yan, Yuling.
- 서명/저자
- Statistical Learning and Optimal Decision Making Under Uncertainty - [electronic resource]
- 발행사항
- [S.l.]: : Princeton University., 2023
- 발행사항
- Ann Arbor : : ProQuest Dissertations & Theses,, 2023
- 형태사항
- 1 online resource(732 p.)
- 주기사항
- Source: Dissertations Abstracts International, Volume: 85-04, Section: B.
- 주기사항
- Advisor: Chen, Yuxin;Fan, Jianqing.
- 학위논문주기
- Thesis (Ph.D.)--Princeton University, 2023.
- 사용제한주기
- This item must not be sold to any third party vendors.
- 초록/해제
- 요약Recent years have witnessed an explosion of interest in designing statistical and decision making algorithms that are computationally efficient and statistically accurate, along with quantitative measures of uncertainty or risk. In this thesis, we make contribution towards this end for several widely encountered problems in statistics, machine learning, and data science. • Starting with estimation algorithms, we show that a principled convex program achieves near-optimal statistical accuracy for robust PCA (i.e., low-rank matrix estimation in the presence of noise, missing data and outliers). We also design an efficient gradient descent algorithm for computing the nonparametric MLE of Gaussian mixture models with provable convergence guarantees.• In terms of uncertainty quantification for estimation algorithms, under a spiked covariance model, we propose a novel approach for performing valid statistical inference for PCA, which enables computation of both confidence regions for the principal subspace and entrywise confidence intervals for the covariance matrix.• Finally, for decision making problems, we develop two efficient offline reinforcement learning algorithms, which cover both the single- and multi-agent case respectively, that achieves optimal sample complexity in finding optimal policy or Nash equilibrium. In addition, we also design an Isotonic Mechanism to enhance peer review in machine learning and artificial intelligence conferences.All of this is enabled by an integrated consideration of statistics, optimization, and decision theory, and requires bringing together tools from a broad spectrum of foundational areas including random matrix theory, high-dimensional probability, PDE, Riemannian geometry, stochastic process, and game theory.
- 일반주제명
- Statistics.
- 키워드
- Decision making
- 기타저자
- Princeton University Operations Research and Financial Engineering
- 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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■00520240214101246
■006m o d
■007cr#unu||||||||
■020 ▼a9798380413930
■035 ▼a(MiAaPQ)AAI30529232
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a310
■1001 ▼aYan, Yuling.
■24510▼aStatistical Learning and Optimal Decision Making Under Uncertainty▼h[electronic resource]
■260 ▼a[S.l.]:▼bPrinceton University. ▼c2023
■260 1▼aAnn Arbor :▼bProQuest Dissertations & Theses, ▼c2023
■300 ▼a1 online resource(732 p.)
■500 ▼aSource: Dissertations Abstracts International, Volume: 85-04, Section: B.
■500 ▼aAdvisor: Chen, Yuxin;Fan, Jianqing.
■5021 ▼aThesis (Ph.D.)--Princeton University, 2023.
■506 ▼aThis item must not be sold to any third party vendors.
■520 ▼aRecent years have witnessed an explosion of interest in designing statistical and decision making algorithms that are computationally efficient and statistically accurate, along with quantitative measures of uncertainty or risk. In this thesis, we make contribution towards this end for several widely encountered problems in statistics, machine learning, and data science. • Starting with estimation algorithms, we show that a principled convex program achieves near-optimal statistical accuracy for robust PCA (i.e., low-rank matrix estimation in the presence of noise, missing data and outliers). We also design an efficient gradient descent algorithm for computing the nonparametric MLE of Gaussian mixture models with provable convergence guarantees.• In terms of uncertainty quantification for estimation algorithms, under a spiked covariance model, we propose a novel approach for performing valid statistical inference for PCA, which enables computation of both confidence regions for the principal subspace and entrywise confidence intervals for the covariance matrix.• Finally, for decision making problems, we develop two efficient offline reinforcement learning algorithms, which cover both the single- and multi-agent case respectively, that achieves optimal sample complexity in finding optimal policy or Nash equilibrium. In addition, we also design an Isotonic Mechanism to enhance peer review in machine learning and artificial intelligence conferences.All of this is enabled by an integrated consideration of statistics, optimization, and decision theory, and requires bringing together tools from a broad spectrum of foundational areas including random matrix theory, high-dimensional probability, PDE, Riemannian geometry, stochastic process, and game theory.
■590 ▼aSchool code: 0181.
■650 4▼aStatistics.
■653 ▼aReinforcement learning algorithms
■653 ▼aStatistical learning
■653 ▼aDecision making
■653 ▼aGaussian mixture models
■690 ▼a0463
■690 ▼a0796
■690 ▼a0800
■71020▼aPrinceton University▼bOperations Research and Financial Engineering.
■7730 ▼tDissertations Abstracts International▼g85-04B.
■773 ▼tDissertation Abstract International
■790 ▼a0181
■791 ▼aPh.D.
■792 ▼a2023
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T16933435▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
■980 ▼a202402▼f2024
