STATISTICAL INFERENCE ACROSS MULTIPLE NETWORKS: ADVANCEMENTS IN MULTIPLEX GRAPH MATCHING AND JOINT SPECTRAL NETWORK EMBEDDINGS

Author:

Pantazis, Konstantinos [claim]

Description:

Networks are commonly used to model and study complex systems that arise in a variety of scientific domains.One important network data modality is multiplex networks which are comprised of a collection of networks over a common vertex set. Multiplex networks can describe complex relational data where edges within each network can encode different relationship or interaction types. With the rise of network modeling of complex, multi-sample network data, there has been a recent emphasis on multiplex inference methods. In this thesis, we develop novel theory and methodology to study underlying network structures and perform statistical inference on multiple networks. While each chapter of the thesis has its own individual merit, synergistically they constitute a coherent multi-scale spectral network inference framework that accounts for unlabeled and correlated multi-sample network data. Together, these results significantly extend the reach of such procedures in the literature. In the first part of the thesis, we consider the inference task of aligning the vertices across a pair of multiplex networks, a key algorithmic step in routines that assume a priori node-aligned data. This general multiplex matching framework is then adapted to the task of detecting a noisy induced multiplex template network in a larger multiplex background network.Our methodology, which lifts the classical graph matching framework and the matched filters method of Sussman et al. (2018) to the multiple network setting, uses the template network to search for the ``most" similar subgraph(s) in the background network, where the notion of similarity is measured via a multiplex graph matching distance. We present an algorithm which can efficiently match the template to a (induced or not induced) subgraph in the background that approximately minimizes a suitable graph matching distance, and we demonstrate the effectiveness of our approach both theoretically and empirically in synthetic and real-world data settings. In the second part of the ...

Contributors:

Lyzinski, Vince ; Digital Repository at the University of Maryland ; University of Maryland (College Park, Md.) ; Mathematics

Year of Publication:

2022

Document Type:

Dissertation ; [Doctoral and postdoctoral thesis]

Language:

Subjects:

Statistics ; Applied mathematics ; Computer science ; Induced correlation ; Joint embeddings ; Latent space network models ; Multiplex graph matching ; Multiscale graph inference ; Time series of networks

DDC:

006 Special computer methods (computed)

Relations:

https://doi.org/10.13016/4gli-r3pp ; http://hdl.handle.net/1903/28981

URL:

http://hdl.handle.net/1903/28981
https://doi.org/10.13016/4gli-r3pp

Content Provider:

University of Maryland: Digital Repository (DRUM)