A Geometric Approach for Inference on Graphical Models
Date
2009
Author
Advisors
Wolpert, Robert L
Mukherjee, Sayan
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Abstract
We formulate a novel approach to infer conditional independence models or Markov structure
of a multivariate distribution. Specifically, our objective is to place informative
prior distributions over graphs (decomposable and unrestricted) and sample efficiently
from the induced posterior distribution. We also explore the idea of factorizing according
to complete sets of a graph; which implies working with a hypergraph that cannot be
retrieved from the graph alone. The key idea we develop in this paper is a parametrization
of hypergraphs using the geometry of points in $R^m$. This induces informative priors
on graphs from specified priors on finite sets of points. Constructing hypergraphs
from finite point sets has been well studied in the fields of computational topology
and random geometric graphs. We develop the framework underlying this idea and illustrate
its efficacy using simulations.
Type
DissertationDepartment
Statistical SciencePermalink
https://hdl.handle.net/10161/1354Citation
Lunagomez, Simon (2009). A Geometric Approach for Inference on Graphical Models. Dissertation, Duke University. Retrieved from https://hdl.handle.net/10161/1354.Collections
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