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Title: Model Selection for Graphical Markov Models
Keywords: Graphical Models, LASSO, Undirected graph, Directed Acyclic graph, Model selection, group LARS
Issue Date: 24-Jan-2014
Citation: ONG MENG HWEE, VICTOR (2014-01-24). Model Selection for Graphical Markov Models. ScholarBank@NUS Repository.
Abstract: In recent times, methods to select a suitable graphical Markov model for a given dataset has been a popular topic of discussion. In this thesis, we consider several issues in graphical Markov model selection. First, we consider a group LARS based method to select undirected graphs. This "Edge selection" algorithm maintains a symmetry in the selected adjacency matrix required for an undirected graph. The method is illustrated through a detailed simulation study and has been applied to real datasets. Next, we consider a LASSO based penalization method when the model is partially known. We consider conditions for selection consistency for such models. It is seen that these consistency conditions are different from the corresponding conditions when the model is completely unknown. In the last section we look at some "almost qualitative" inequalities among the signed partial correlation and regression coefficients between the vertices on a graph.
Appears in Collections:Ph.D Theses (Open)

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