dc.contributor.advisor Athreya, Avanti en_US dc.contributor.author Pao, Henry en_US dc.date.accessioned 2015-09-16T03:36:19Z dc.date.available 2015-09-16T03:36:19Z dc.date.created 2015-05 en_US dc.date.issued 2015-01-26 en_US dc.date.submitted May 2015 en_US dc.identifier.uri http://jhir.library.jhu.edu/handle/1774.2/37911 dc.description.abstract Graphs are widely used in many fields of research, ranging from natural sciences to computer and mathematical sciences. Graph inference is an area of intense research. In this dissertation, we propose several methodologies in graph inference. We focus on statistical inference using graph invariants, vertex nomination, and a divide-and-conquer graph matching technique. We present a comparative power analysis of various graph invariants for testing the hypothesis that the graph has a subgraph with higher edge probability. Given a graph drawn from a kidney-egg random graph model, the null hypothesis is that all edge probabilities are equal. The alternative hypothesis is that there exists a subset of vertices which are more likely to be adjacenct to each other than the rest of the graph. Using Monte Carlo simulations, we estimate the power of several graph invariants acting as test statistics. We discovered that for many choices of parameters in the random graph model, the scan statistic and clustering coefficient often dominate other graph invariants. However, our results indicates that none of the graph invariants considered is uniformly most powerful. Given a graph drawn from a stochastic block model where one block is of particular interest, vertex nomination is the task of creating a list of vertices such that there are an abundance of vertices from the block of interest at the top of the list. Vertex nomination is useful in situations where only a limited number of vertices can be examined and have their block membership checked. We propose several vertex nomination schemes, derive theoretical results for performance, and compare the schemes on simulated and real data. Given two graphs, graph matching is to create a mapping from one set of vertices to the other, such that the edge structure of the graphs is preserved as best as possible. We develop a new method for scaling graph matching algorithms, and prove performance guarantees. Any graph matching algorithm can be scaled using our divide-and-conquer technique. The performance of this technique is demonstrated on large simulated graphs and human brain graphs. en_US dc.format.mimetype application/pdf en_US dc.language en dc.publisher Johns Hopkins University dc.subject Graph en_US dc.subject graph inference en_US dc.subject graph matching en_US dc.subject vertex nomination en_US dc.subject metropolis-hastings en_US dc.subject spectral embedding en_US dc.subject spectral partitioning en_US dc.subject parallelization en_US dc.subject divide and conquer en_US dc.subject en_US dc.title Graph Inference and Graph Matching en_US dc.type Thesis en_US thesis.degree.discipline Applied Mathematics & Statistics en_US thesis.degree.grantor Johns Hopkins University en_US thesis.degree.grantor Whiting School of Engineering en_US thesis.degree.level Doctoral en_US thesis.degree.name Ph.D. en_US dc.type.material text en_US thesis.degree.department Applied Mathematics and Statistics en_US dc.contributor.committeeMember Fishkind, Donniell E. en_US dc.contributor.committeeMember Priebe, Carey E. en_US dc.contributor.committeeMember Lyzinski, Vince en_US
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