Bayesian approach to shrinkage estimation for large scale vector autoregressive models = 대규모 벡터자기회귀모형을 위한 축소추정의 베이즈 접근법

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A vector autoregressive (VAR) model is a statistical model that describes linear dependencies among vectors of current and previous values for multivariate time series data. Recently, there has been increasing demand to employ high-dimensional VAR models that can process large numbers of time series variables from areas such as systems biology, econometrics, and computational neuroscience. However, when the number of variables is too large compared to the limited length of the time series, computational obstacles, including singular matrix problems and overfitting, are encountered. Several methods have been proposed in literature to handle high-dimensional sparse data problems, but most have limited applications because of heavy computational costs and incorrect assumptions about data. In this thesis we propose a Bayesian approach for modeling VAR processes in order to incorporate proper dependence assumptions and deal with a large dimensionality of data with low computational costs. For the selection of the shrinkage parameter, which is regarded as a prior hyperparameter, we propose a new score function related to the limit of a marginal posterior distribution for the model coefficients. The proposed shrinkage is computationally carried out by using a variation of cross validation. Experimental results based on simulated data demonstrate that the suggested method performs better than the other methods reported in the literature when (1) the number of variables is large and the length of time series is small, or (2) there are strong cross correlations between the time series variables. The proposed method is applied to real world data from systems biology and computational neuroscience. In both cases, the time series data contain limited numbers of observations with relatively large numbers of variables. Once a VAR model is estimated by the proposed method, the model structure that is determined based on nonzero VAR coefficients is discovered by further pruni...
Advisors
Kim, Sung-Horesearcher김성호
Description
한국과학기술원 : 수리과학과,
Publisher
한국과학기술원
Issue Date
2013
Identifier
513601/325007  / 020065115
Language
eng
Description

학위논문(박사) - 한국과학기술원 : 수리과학과, 2013.2, [ vi, 71 p. ]

Keywords

Bayesian regression; cross validation; high-dimensional data; shrinkage estimation; 베이즈 추정; 교차 검정; 고차원 자료; 축소 추정; fMRI; fMRI

URI
http://hdl.handle.net/10203/181551
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=513601&flag=dissertation
Appears in Collection
MA-Theses_Ph.D.(박사논문)
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