Statistical methods on graphs

Abstract/Contents

Abstract

In relational data the most basic statistical questions focus on modeling the structure of the network and on making inferences about the nodes. These questions are addressed separately with a simple but novel model for each. On the side of graph structure, a class of "monotone random graphs" are examined where n vertices are totally ordered such that independent edge probabilities satisfy the partial ordering p_{i, j} ≤ p_{k, l} for i ≤ k and j ≤ l. The MLE of the graph's edge parameters can be solved by isotonic regression (equivalent to projection onto a convex cone), and this MLE is a consistent estimator. On the nodal inference side, the focus is specifically on multi-relational networks. This approach constructs a design matrix by multiplying a vector of nodal features with each adjacency matrix in which the nodes are embedded. After constructing this design matrix through nodal diffusion, standard statistical learning techniques can be applied to the design matrix.

Description

Type of resource	text
Form	electronic; electronic resource; remote
Extent	1 online resource.
Publication date	2014
Issuance	monographic
Language	English

Creators/Contributors

Associated with	Head, Austen
Associated with	Stanford University, Department of Statistics.
Primary advisor	Holmes, Susan
Thesis advisor	Holmes, Susan
Thesis advisor	Chatterjee, Sourav
Thesis advisor	Diaconis, Persi
Advisor	Chatterjee, Sourav
Advisor	Diaconis, Persi

Subjects

Genre	Theses

Bibliographic information

Statement of responsibility	Austen Head.
Note	Submitted to the Department of Statistics.
Thesis	Thesis (Ph.D.)--Stanford University, 2014.
Location	electronic resource

Access conditions

Copyright

© 2014 by Austen Wallace Head

License

This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).

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