DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | Park, Jinkyoo | - |
dc.contributor.advisor | 박진규 | - |
dc.contributor.author | 이승훈 | - |
dc.date.accessioned | 2022-04-21T19:31:15Z | - |
dc.date.available | 2022-04-21T19:31:15Z | - |
dc.date.issued | 2020 | - |
dc.identifier.uri | http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=986316&flag=dissertation | en_US |
dc.identifier.uri | http://hdl.handle.net/10203/295316 | - |
dc.description | 학위논문(석사) - 한국과학기술원 : 산업및시스템공학과, 2020.2,[iii, 30 p. :] | - |
dc.description.abstract | Stochastic differential equations (SDEs) are flexible models for describing system behaviors from various contexts. We propose a way to adopt the Gaussian process regression method to approximate the conditional probability distribution of the state vector whose evolution is described by SDE with linear drift. We mathematically derive the exact covariance structure of a multi-dimensional diffusion process with linear drift, and use it as a kernel function in multi-output Gaussian process regression. The usage of our approach differs according to the knowledge regarding the parameters in SDE. For the case when the coefficients of the SDEs are known, we firstly compare our approach with sampling-based methodologies for estimating the conditional probability distribution of diffusion processes by taking Cox-Ingersoll-Ross model as an example. The results show that our approach is consistent with sampling algorithms considering the estimated mean and variance. We then illustrate how to adopt our approach when the coefficients of the SDEs are unknown. We compare the performance of Gaussian process regression with the kernel function we derived to those with conventional kernel candidates. When applied to multi-dimensional Ornstein-Uhlenbeck process and inlet/outlet pressure data from gas regulators, our method considerably reduces the mean square error of prediction tasks, especially when there is information that comes across dimensions. | - |
dc.language | eng | - |
dc.publisher | 한국과학기술원 | - |
dc.subject | Multi-output Gaussian process regression▼akernel trick▼astochastic differential equation▼amultivariate diffusion bridge▼adiffusion bridge | - |
dc.subject | 다차원 정규 과정 회귀▼a공분산 함수▼a확률 미분 방정식▼a다차원 확산 과정▼a확산 과정 | - |
dc.title | Gaussian process regression of conditioned linear-drift diffusion process | - |
dc.title.alternative | 조건부 선형 추세 확산 과정의 정규 확률 과정 회귀 | - |
dc.type | Thesis(Master) | - |
dc.identifier.CNRN | 325007 | - |
dc.description.department | 한국과학기술원 :산업및시스템공학과, | - |
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.