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bayesian lasso with Neighborhood Regression Method for Gaussian Graphical Model

Acta Mathematicae Applicatae Sinica 2017年第2期33卷 485-496页

作者： Fan-qun LI Xin-sheng ZHANG Department of Statistics School of Management Fudan University Institute of Statistics and Applied Mathematics Anhui University of Finance and Economics

In this paper, we consider the problem of estimating a high dimensional precision matrix of Gaussian graphical model. Taking advantage of the connection between multivariate linear regression and entries of the precision matrix, we propose bayesian lasso together with neighborhood regression estimate for Gaussian graphical model. This method can obtain parameter estimation and model selection simultaneously. Moreover, the proposed method can provide symmetric confidence intervals of all entries of the precision matrix.

关键词： gaussian graphical model regression precision matrix bayesian lasso Frobenius loss

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bayesian lasso for Screening Experiments

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Journal of Mathematics and System Science 2013年第2期3卷 68-74页

作者： Hidehisa Noguchi Yoshikazu Ojima Seiichi Yasui Department of Industrial Science and Technology Tokyo University of Science Chiba 2788510 Japan

The purpose of variable selection is to identify important predictors for response variables. Although there are many varieties of variable selection methods, almost all of them have a problem of not accounting for the relationship between predictors. Therefore it would well happen that the selected subset of identified predictors leads to hard-to-interpret model consisted of only interaction terms. In design of experiments, the analysis is driven by the effect heredity principle which governs the relationship between an interaction and its corresponding main effects. In this paper, the authors extend the variable selection method the lasso with effect heredity principle to its bayesian version. In the example, the authors analyze the data obtained from typical screening design Plackett-Bunnan design and compare the result from the ordinary bayesian lasso and proposed method.

关键词： Variable selection bayesian lasso effect heredity principle.

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