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From EM to Depth Estimators: An Overparametrization View
From EM to Depth Estimators: An Overparametrization View
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20260202103026
- ISBN
- 9798286441334
- DDC
- 310
- 저자명
- Liu, Jiyi.
- 서명/저자
- From EM to Depth Estimators: An Overparametrization View
- 발행사항
- [Sl] : Yale University, 2025
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2025
- 형태사항
- 111 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 86-12, Section: B.
- 주기사항
- Advisor: Zhou, Harrison.
- 학위논문주기
- Thesis (Ph.D.)--Yale University, 2025.
- 초록/해제
- 요약This paper introduces the heated idea of overparametrization in the field of neural nets training into the statistical scenario, establishes the theoretical properties of the overparameterized Expectation-Maximization (EM) algorithm and its connections to deep learning and robust statistics. We establish a global convergence result for overparameterized EM in Gaussian mixture models (GMMs), demonstrating that overparameterization reshapes the optimization landscape and facilitates convergence. Inspired by its success in deep learning, we show that overparameterized EM mitigates initialization sensitivity while maintaining statistical consistency.Beyond EM, we introduce the Penalized Tangent Depth (PTD) estimator, a novel framework linking GAN training and depth-based robust estimation. PTD provides a unified approach to robust inference, offering computational efficiency and statistical robustness under contamination. Our findings highlight fundamental connections between adversarial learning and classical robustness theory.Several open problems remain, including a rigorous proof of unconditional EM convergence, statistical efficiency in high-dimensional settings, and other settings beyond the robustness. Future research may further explore the interplay between overparameterized EM, gradient-based learning, and adversarial robustness. Our results contribute to bridging classical statistical methods with modern machine learning theory, providing new insights into optimization, robustness, and inference.
- 일반주제명
- Statistics
- 일반주제명
- Applied mathematics
- 일반주제명
- Computer science
- 기타저자
- Yale University Statistics and Data Science
- 기본자료저록
- Dissertations Abstracts International. 86-12B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■006m o d
■007cr#unu||||||||
■020 ▼a9798286441334
■035 ▼a(MiAaPQ)AAI31845305
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a310
■1001 ▼aLiu, Jiyi.
■24510▼aFrom EM to Depth Estimators: An Overparametrization View
■260 ▼a[Sl]▼bYale University▼c2025
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2025
■300 ▼a111 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 86-12, Section: B.
■500 ▼aAdvisor: Zhou, Harrison.
■5021 ▼aThesis (Ph.D.)--Yale University, 2025.
■520 ▼aThis paper introduces the heated idea of overparametrization in the field of neural nets training into the statistical scenario, establishes the theoretical properties of the overparameterized Expectation-Maximization (EM) algorithm and its connections to deep learning and robust statistics. We establish a global convergence result for overparameterized EM in Gaussian mixture models (GMMs), demonstrating that overparameterization reshapes the optimization landscape and facilitates convergence. Inspired by its success in deep learning, we show that overparameterized EM mitigates initialization sensitivity while maintaining statistical consistency.Beyond EM, we introduce the Penalized Tangent Depth (PTD) estimator, a novel framework linking GAN training and depth-based robust estimation. PTD provides a unified approach to robust inference, offering computational efficiency and statistical robustness under contamination. Our findings highlight fundamental connections between adversarial learning and classical robustness theory.Several open problems remain, including a rigorous proof of unconditional EM convergence, statistical efficiency in high-dimensional settings, and other settings beyond the robustness. Future research may further explore the interplay between overparameterized EM, gradient-based learning, and adversarial robustness. Our results contribute to bridging classical statistical methods with modern machine learning theory, providing new insights into optimization, robustness, and inference.
■590 ▼aSchool code: 0265.
■650 4▼aStatistics
■650 4▼aApplied mathematics
■650 4▼aComputer science
■653 ▼aPenalized Tangent Depth
■653 ▼aTheoretical properties
■653 ▼aExpectation-Maximization
■653 ▼aStatistical efficiency
■653 ▼aGradient-based learning
■690 ▼a0463
■690 ▼a0984
■690 ▼a0800
■690 ▼a0364
■71020▼aYale University▼bStatistics and Data Science.
■7730 ▼tDissertations Abstracts International▼g86-12B.
■790 ▼a0265
■791 ▼aPh.D.
■792 ▼a2025
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17356737▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
