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On the Statistical Properties of Deep Learners for Intrinsically Low Dimensional Data
On the Statistical Properties of Deep Learners for Intrinsically Low Dimensional Data
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20260202103537
- ISBN
- 9798288863813
- DDC
- 310
- 서명/저자
- On the Statistical Properties of Deep Learners for Intrinsically Low Dimensional Data
- 발행사항
- [Sl] : University of California, Berkeley, 2025
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2025
- 형태사항
- 230 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 87-01, Section: B.
- 주기사항
- Advisor: Bartlett, Peter L.
- 학위논문주기
- Thesis (Ph.D.)--University of California, Berkeley, 2025.
- 초록/해제
- 요약The advent of deep learning has completely revolutionized both supervised and unsupervised machine learning to obtain super-human performance across all fields of modern science. However, despite the remarkable empirical successes of deep learners, the theoretical guarantees for their statistical accuracy remain rather pessimistic. In particular, the data distributions on which deep learners are generally applied, such as natural images, are often hypothesized to have an intrinsic low-dimensional structure in a typically high-dimensional feature space, but this is often not reflected in the derived rates in the state-of-the-art analyses. The aim of this thesis is to bridge the gap between the theory and practice of deep learning from a statistical perspective. We demonstrate that deep learners exhibit a convergence rate determined solely by the intrinsic dimensionality of the data, rather than its nominal high-dimensional feature representation. Our work not only provides practical guidelines for selecting suitable network architectures but also connects the theoretical analyses of these models to established convergence rates in optimal transport and non-parametric statistics literature. In this thesis, we derive the sharpest convergence rates for various learning scenarios, including Generative Adversarial Networks (GANs), Wasserstein Autoencoders (WAEs), federated learning, cycle-consistent GANs, Bi-directional GANs, and deep supervised learners characterized by an exponential family dependency structure. Furthermore, we introduce a novel measure to characterize the intrinsic dimension of probability measures and achieve the sharpest known approximation results for neural networks employing Rectified Linear Unit (ReLU) activation, improving upon classical benchmarks.
- 일반주제명
- Statistics
- 일반주제명
- Computer science
- 일반주제명
- Information technology
- 키워드
- Minimax rates
- 기타저자
- University of California, Berkeley Statistics
- 기본자료저록
- Dissertations Abstracts International. 87-01B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■006m o d
■007cr#unu||||||||
■020 ▼a9798288863813
■035 ▼a(MiAaPQ)AAI32040560
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a310
■1001 ▼aChakraborty, Saptarshi.
■24510▼aOn the Statistical Properties of Deep Learners for Intrinsically Low Dimensional Data
■260 ▼a[Sl]▼bUniversity of California, Berkeley▼c2025
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2025
■300 ▼a230 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 87-01, Section: B.
■500 ▼aAdvisor: Bartlett, Peter L.
■5021 ▼aThesis (Ph.D.)--University of California, Berkeley, 2025.
■520 ▼aThe advent of deep learning has completely revolutionized both supervised and unsupervised machine learning to obtain super-human performance across all fields of modern science. However, despite the remarkable empirical successes of deep learners, the theoretical guarantees for their statistical accuracy remain rather pessimistic. In particular, the data distributions on which deep learners are generally applied, such as natural images, are often hypothesized to have an intrinsic low-dimensional structure in a typically high-dimensional feature space, but this is often not reflected in the derived rates in the state-of-the-art analyses. The aim of this thesis is to bridge the gap between the theory and practice of deep learning from a statistical perspective. We demonstrate that deep learners exhibit a convergence rate determined solely by the intrinsic dimensionality of the data, rather than its nominal high-dimensional feature representation. Our work not only provides practical guidelines for selecting suitable network architectures but also connects the theoretical analyses of these models to established convergence rates in optimal transport and non-parametric statistics literature. In this thesis, we derive the sharpest convergence rates for various learning scenarios, including Generative Adversarial Networks (GANs), Wasserstein Autoencoders (WAEs), federated learning, cycle-consistent GANs, Bi-directional GANs, and deep supervised learners characterized by an exponential family dependency structure. Furthermore, we introduce a novel measure to characterize the intrinsic dimension of probability measures and achieve the sharpest known approximation results for neural networks employing Rectified Linear Unit (ReLU) activation, improving upon classical benchmarks.
■590 ▼aSchool code: 0028.
■650 4▼aStatistics
■650 4▼aComputer science
■650 4▼aInformation technology
■653 ▼aDeep learning theory
■653 ▼aGeneralization bounds
■653 ▼aIntrinsic dimension
■653 ▼aMinimax rates
■653 ▼aNeural network approximation
■653 ▼aStatistical learning theory
■690 ▼a0463
■690 ▼a0489
■690 ▼a0984
■690 ▼a0800
■71020▼aUniversity of California, Berkeley▼bStatistics.
■7730 ▼tDissertations Abstracts International▼g87-01B.
■790 ▼a0028
■791 ▼aPh.D.
■792 ▼a2025
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17357617▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
