Faculty Advisor or Committee Member

Randy Clinton Paffenroth, Advisor

Faculty Advisor or Committee Member

Luca Capogna

Identifier

etd-012217-230654

Abstract

We address the problem of identifying the neighborhood structure of an undirected graph, whose nodes are labeled with the elements of a multivariate normal (MVN) random vector. A semi-definite program is given for estimating the information matrix under arbitrary constraints on its elements. More importantly, a closed-form expression is given for the maximum likelihood (ML) estimator of the information matrix, under the constraint that the information matrix has pre-specified elements in a given pattern (e.g., in a principal submatrix). The results apply to the identification of dependency labels in a graphical model with neighborhood constraints. This neighborhood structure excludes nodes which are conditionally independent of a given node and the graph is determined by the non- zero elements in the information matrix for the random vector. A cross-validation principle is given for determining whether the constrained information matrix returned from this procedure is an acceptable model for the information matrix, and as a consequence for the neighborhood structure of the Markov Random Field (MRF) that is identified with the MVN random vector.

Publisher

Worcester Polytechnic Institute

Degree Name

MS

Department

Mathematical Sciences

Project Type

Thesis

Date Accepted

2017-01-22

Accessibility

Unrestricted

Subjects

Closed Form Solutions, Convex Optimization, Information Matrix, Graphical Models

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