• Journal of the Korean Data and Information Science Society
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• v.25 no.4
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• pp.881-891
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• 2014

Graphical models can be used as an intuitive tool for modeling a complex stochastic system with a large number of variables related each other because the conditional independence between random variables can be visualized as a network. Graphical least absolute shrinkage and selection operator (LASSO) is considered to be effective in avoiding overfitting in the estimation of Gaussian graphical models for high dimensional data. In this paper, we consider the model selection problem in graphical LASSO. Particularly, we compare various model selection criteria via simulations and analyze a real financial data set.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.9 no.5
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• pp.1249-1254
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• 2008

The crucial part of graphical model is to compute the posterior distribution of parameters plus with the hidden variables given the observed data. In this paper, implementation of variational Bayes method for Gaussian mixture model and derivation of factorial variational approximation have been proposed. This result can be used for data analysis tasks like information retrieval or data visualization.

• Journal of Plant Biotechnology
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• v.38 no.2
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• pp.162-168
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• 2011

High salinity is a common stress condition that adversely affects plant growth and crop production. In response to various environmental stresses, plants activate a number of defense genes that function to increase the tolerance. To isolate Arabidopsis genes that are involved in abiotic stress responses, we carried out genetic screening using various mutant lines. Among them, the blh8 ($\b{B}$EL1-$\b{L}$ike $\b{H}$omeodomain $\underline{8}$) mutant specifically shows chlorotic phenotypes to ionic (specifically, $Na^+$ and $K^+$) stresses, but no differences in root growth. In addition, BLH8 is related to plant development and abiotic stress as predicted by a Graphical Gaussian Model (GGM) network program. It implies that BLH8 functions as a putative transcription factor related to abiotic stress responses. Collectively, our results show that gene network analysis is a useful tool for isolating genes involved in stress adaptation in plants.

• Journal of Communications and Networks
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• v.12 no.4
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• pp.289-307
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• 2010

The problem of model selection arises in a number of contexts, such as subset selection in linear regression, estimation of structures in graphical models, and signal denoising. This paper studies non-asymptotic model selection for the general case of arbitrary (random or deterministic) design matrices and arbitrary nonzero entries of the signal. In this regard, it generalizes the notion of incoherence in the existing literature on model selection and introduces two fundamental measures of coherence-termed as the worst-case coherence and the average coherence-among the columns of a design matrix. It utilizes these two measures of coherence to provide an in-depth analysis of a simple, model-order agnostic one-step thresholding (OST) algorithm for model selection and proves that OST is feasible for exact as well as partial model selection as long as the design matrix obeys an easily verifiable property, which is termed as the coherence property. One of the key insights offered by the ensuing analysis in this regard is that OST can successfully carry out model selection even when methods based on convex optimization such as the lasso fail due to the rank deficiency of the submatrices of the design matrix. In addition, the paper establishes that if the design matrix has reasonably small worst-case and average coherence then OST performs near-optimally when either (i) the energy of any nonzero entry of the signal is close to the average signal energy per nonzero entry or (ii) the signal-to-noise ratio in the measurement system is not too high. Finally, two other key contributions of the paper are that (i) it provides bounds on the average coherence of Gaussian matrices and Gabor frames, and (ii) it extends the results on model selection using OST to low-complexity, model-order agnostic recovery of sparse signals with arbitrary nonzero entries. In particular, this part of the analysis in the paper implies that an Alltop Gabor frame together with OST can successfully carry out model selection and recovery of sparse signals irrespective of the phases of the nonzero entries even if the number of nonzero entries scales almost linearly with the number of rows of the Alltop Gabor frame.