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Efficient Robust Algorithms for Linear Discriminant Analysis and Sequential Matching Problems
Efficient Robust Algorithms for Linear Discriminant Analysis and Sequential Matching Problems
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20260209102910
- ISBN
- 9798265401427
- DDC
- 330
- 저자명
- Shi, Yuyang.
- 서명/저자
- Efficient Robust Algorithms for Linear Discriminant Analysis and Sequential Matching Problems
- 발행사항
- [Sl] : Georgia Institute of Technology, 2023
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2023
- 형태사항
- 139 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 87-05, Section: B.
- 주기사항
- Advisor: Mei, Yajun.
- 학위논문주기
- Thesis (Ph.D.)--Georgia Institute of Technology, 2023.
- 초록/해제
- 요약Data science, machine learning, or statistics are useful to assist making data-driven decisions in many modern applications, and some challenges rise in analyzing real-world data sets such as high-dimensionality, robustness, and computational efficiency. This dissertation investigates three specific topics in statistical machine learning: (1) pivotal method for high-dimensional linear discriminant analysis (LDA); (2) robust algorithm for LDA under data contamination; and (3) efficient algorithm for sequential assignment with unknown utility.In Chapter 1, we propose a pivotal method for high-dimensional linear discriminant analysis (LDA) that enjoys tuning-insensitive property. We term our method as PivotAl LiNear Discriminant Analysis (PANDA). Our method conducts parameter estimation under a pivotal estimation framework and only needs to solve a single convex optimization problem when both means and variances are unknown for both classes of training data. Theoretically, our method achieves comparable convergence rates as existing methods in terms of both estimation error and misclassification rate.In Chapter 2, we propose a computationally efficient algorithm for robust LDA under data contamination, where a fraction of sample data might be corrupted by some adversary. Our main ideas are as follows. We first identify the outliers in each class and robustly estimate the mean, and then apply our developed PANDA method for uncontaminated data to estimate the discriminant direction in LDA with data contamination. Theoretical properties of the proposed algorithm are established in terms of both the error in estimating the optimal projection vector and the misclassification rate.In Chapter 3, we develop an efficient algorithm for sequential assignment with unknown utility, with the objective of nearly maximizing the overall utility for each time. Our proposed algorithm is to use stochastic binary bandit feedback to adaptively estimate the unknown utilities through the logistic regression, and then to combine the Upper Confidence Bound (UCB) algorithm in the multi-armed bandit problem with the Hungarian algorithm in the assignment problem. We derive the theoretical bounds of our algorithm for both the estimation error and the total regret, and numerical studies are also conducted to illustrate the usefulness of our algorithm.We conclude the dissertation in Chapter 4, where we summarize our contributions, and highlight several potential research topics for future investigation.
- 일반주제명
- Sparsity
- 일반주제명
- Leukemia
- 일반주제명
- Normal distribution
- 일반주제명
- Convex analysis
- 일반주제명
- Linear programming
- 일반주제명
- Parameter estimation
- 일반주제명
- Mathematics
- 일반주제명
- Oncology
- 기본자료저록
- Dissertations Abstracts International. 87-05B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■020 ▼a9798265401427
■035 ▼a(MiAaPQ)AAI32315821
■035 ▼a(MiAaPQ)GeorgiaTech75160
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a330
■1001 ▼aShi, Yuyang.
■24510▼aEfficient Robust Algorithms for Linear Discriminant Analysis and Sequential Matching Problems
■260 ▼a[Sl]▼bGeorgia Institute of Technology▼c2023
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2023
■300 ▼a139 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 87-05, Section: B.
■500 ▼aAdvisor: Mei, Yajun.
■5021 ▼aThesis (Ph.D.)--Georgia Institute of Technology, 2023.
■520 ▼aData science, machine learning, or statistics are useful to assist making data-driven decisions in many modern applications, and some challenges rise in analyzing real-world data sets such as high-dimensionality, robustness, and computational efficiency. This dissertation investigates three specific topics in statistical machine learning: (1) pivotal method for high-dimensional linear discriminant analysis (LDA); (2) robust algorithm for LDA under data contamination; and (3) efficient algorithm for sequential assignment with unknown utility.In Chapter 1, we propose a pivotal method for high-dimensional linear discriminant analysis (LDA) that enjoys tuning-insensitive property. We term our method as PivotAl LiNear Discriminant Analysis (PANDA). Our method conducts parameter estimation under a pivotal estimation framework and only needs to solve a single convex optimization problem when both means and variances are unknown for both classes of training data. Theoretically, our method achieves comparable convergence rates as existing methods in terms of both estimation error and misclassification rate.In Chapter 2, we propose a computationally efficient algorithm for robust LDA under data contamination, where a fraction of sample data might be corrupted by some adversary. Our main ideas are as follows. We first identify the outliers in each class and robustly estimate the mean, and then apply our developed PANDA method for uncontaminated data to estimate the discriminant direction in LDA with data contamination. Theoretical properties of the proposed algorithm are established in terms of both the error in estimating the optimal projection vector and the misclassification rate.In Chapter 3, we develop an efficient algorithm for sequential assignment with unknown utility, with the objective of nearly maximizing the overall utility for each time. Our proposed algorithm is to use stochastic binary bandit feedback to adaptively estimate the unknown utilities through the logistic regression, and then to combine the Upper Confidence Bound (UCB) algorithm in the multi-armed bandit problem with the Hungarian algorithm in the assignment problem. We derive the theoretical bounds of our algorithm for both the estimation error and the total regret, and numerical studies are also conducted to illustrate the usefulness of our algorithm.We conclude the dissertation in Chapter 4, where we summarize our contributions, and highlight several potential research topics for future investigation.
■590 ▼aSchool code: 0078.
■650 4▼aSparsity
■650 4▼aLeukemia
■650 4▼aNormal distribution
■650 4▼aConvex analysis
■650 4▼aLinear programming
■650 4▼aParameter estimation
■650 4▼aMathematics
■650 4▼aOncology
■690 ▼a0800
■690 ▼a0405
■690 ▼a0992
■71020▼aGeorgia Institute of Technology.
■7730 ▼tDissertations Abstracts International▼g87-05B.
■790 ▼a0078
■791 ▼aPh.D.
■792 ▼a2023
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17365993▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
