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Probabilistic Models on Fibre Bundles
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| 자료유형 | 학위논문 |
|---|---|
| 서명/저자사항 | Probabilistic Models on Fibre Bundles. |
| 개인저자 | Shan, Shan. |
| 단체저자명 | Duke University. Mathematics. |
| 발행사항 | [S.l.]: Duke University., 2019. |
| 발행사항 | Ann Arbor: ProQuest Dissertations & Theses, 2019. |
| 형태사항 | 124 p. |
| 기본자료 저록 | Dissertations Abstracts International 81-04B. Dissertation Abstract International |
| ISBN | 9781088335062 |
| 학위논문주기 | Thesis (Ph.D.)--Duke University, 2019. |
| 일반주기 |
Source: Dissertations Abstracts International, Volume: 81-04, Section: B.
Advisor: Daubechies, Ingrid. |
| 이용제한사항 | This item must not be sold to any third party vendors. |
| 요약 | In this thesis, we propose probabilistic models on fibre bundles for learning the generative process of data. The main tool we use is the diffusion kernel and we use it in two ways. First, we build from the diffusion kernel on a fibre bundle a projected kernel that generates robust representations of the data, and we test that it outperforms regular diffusion maps under noise. Second, this diffusion kernel gives rise to a natural covariance function when defining Gaussian processes (GP) on the fibre bundle. To demonstrate the uses of GP on a fibre bundle, we apply it to simulated data on a Mobius strip for the problem of prediction and regression. Parameter tuning can also be guided by a novel semi-group test arising from the geometric properties of diffusion kernel. For an example of real-world application, we use probabilistic models on fibre bundles to study evolutionary process on anatomical surfaces. In a separate chapter, we propose a robust algorithm (ariaDNE) for computing curvature on each individual surface. The proposed machinery, relating diffusion processes to probabilistic models on fibre bundles, provides a unified framework for ideas from a variety of different topics such as geometric operators, dimension reduction, regression and Bayesian statistics. |
| 일반주제명 | Mathematics. |
| 언어 | 영어 |
| 바로가기 | 
: 이 자료의 원문은 한국교육학술정보원에서 제공합니다. |
