Abstract Details
Activity Number:
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279
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Type:
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Topic Contributed
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Date/Time:
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Tuesday, August 5, 2014 : 8:30 AM to 10:20 AM
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Sponsor:
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Korean International Statistical Society
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Abstract #312177
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Title:
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Sparse Robust Graphical Models
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Author(s):
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Myung Hee Lee*+ and Hyonho Chun and James Fleet
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Companies:
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Colorado State University and Purdue University and Purdue University
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Keywords:
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graphical model ;
quantile regression ;
conditional independence ;
robust procedure
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Abstract:
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A graphical model is a way of inferring conditional relationships among multiple variables. When the variables follow multivariate normal distribution, we can fit Gaussian Graphical Models (GGMs) and identify the conditional independence relationship by the zero entries of the precision matrix. However, when the variables do not follow Gaussian, the conditional independence can no longer be inferred from the precision matrix. We propose a graphical model that is robust to the distributional assumption, and we do this via applying a set of sparse quantile regression models. We show that the conditional quantile probabilities of one variable as function of the rest bear sufficient information on the conditional dependence between variables under appropriate assumption. We demonstrate the advantages of our approach using simulation study under various scenarios and then we apply our method to an interesting real biological dataset, where considerable amount of the dataset is contaminated, illustrating the advantage of the proposed method in a real setting.
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