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Bayesian curve fitting for discontinuous functions using overcomplete system with multiple kernels
다중커널 과완비 체계를 이용한 불연속 함수의 베이즈 함수 추정

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dc.contributor.advisor이재용-
dc.contributor.author이영선-
dc.date.accessioned2018-05-28T17:13:08Z-
dc.date.available2018-05-28T17:13:08Z-
dc.date.issued2018-02-
dc.identifier.other000000150856-
dc.identifier.urihttp://hdl.handle.net/10371/141156-
dc.description학위논문 (박사)-- 서울대학교 대학원 : 자연과학대학 통계학과, 2018. 2. 이재용.-
dc.description.abstractWe propose a Bayesian model for estimating functions that may have jump discontinuities, and variational method for inference. The proposed model is an extension of the LARK model, which enables functions to be represented by the small number of elements from an overcomplete system composing of multiple kernels. The location of jumps, the number of elements, and even the smoothness of functions are automatically determined by the Levy random measure, there is no need for model selection. A simulation study and a real data analysis illustrate that the proposed model performs better than the standard nonparametric models for the estimation of discontinuous functions and show the suggested variational method significantly reduces the computation time than the conventional inference method, reversible jump Markov chain Monte Carlo. Finally, we prove prior positivity of the model and show that the prior has sufficiently large support including discontinuous functions with finite number of jumps.-
dc.description.tableofcontents1 Introduction 1
1.1 Nonparametric Bayesian regression model 1
1.2 Literature review of nonparametric function estimation 3
1.3 Literature review of nonparametric function estimation for functions with jumps 8
2 Bayesian curve fitting for discontinuous functions using overcomplete system with multiple kernels 11
2.1 Introduction 11
2.2 The LARK model 12
2.3 Levy adaptive regression with mutiple kernels (LARMuK) 16
2.3.1 Structure of proposed model 16
2.3.2 Prior 19
2.4 Algorithm 27
2.5 Data analysis 32
2.5.1 Simulation data analysis 33
2.5.2 Real data analysis 41
2.6 Discussion 46
3 Stochastic variational inference for the LARMuK model 48
3.1 Introduction 48
3.2 Variational method in general 49
3.2.1 The relationship with EM method 56
3.3 Simulated annealing 59
3.4 Stochastic variational method for the LARMuK model 61
3.4.1 The ELBO 61
3.4.2 Updating variational parameters 70
3.5 Data analysis 76
3.5.1 Simulation data analysis 77
3.5.2 Real data analysis 81
3.6 Discussion 83
Bibliography 84
Abstract in Korean 89
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dc.formatapplication/pdf-
dc.format.extent4890888 bytes-
dc.format.mediumapplication/pdf-
dc.language.isoen-
dc.publisher서울대학교 대학원-
dc.subjectBayesian nonparametric regression-
dc.subjectovercomplete system-
dc.subjectmultiple kernel-
dc.subjectLevy random measure-
dc.subjectPoisson random measure-
dc.subjectvariational method-
dc.subjectsimulated annealing-
dc.subject.ddc519.5-
dc.titleBayesian curve fitting for discontinuous functions using overcomplete system with multiple kernels-
dc.title.alternative다중커널 과완비 체계를 이용한 불연속 함수의 베이즈 함수 추정-
dc.typeThesis-
dc.contributor.AlternativeAuthorLee Youngseon-
dc.description.degreeDoctor-
dc.contributor.affiliation자연과학대학 통계학과-
dc.date.awarded2018-02-
Appears in Collections:
College of Natural Sciences (자연과학대학)Dept. of Statistics (통계학과)Theses (Ph.D. / Sc.D._통계학과)
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