Date of Award

Spring 1-1-2019

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

First Advisor

Aaron Clauset

Second Advisor

Cristopher Moore

Third Advisor

Aram Galstyan

Fourth Advisor

Paul Constantine

Fifth Advisor

Daniel Larremore

Abstract

Relational data has become increasingly ubiquitous nowadays. Networks are very rich tools in graph theory, which represent real world interactions through a simple abstract graph, including nodes and edges. Network analysis and modeling has gained extremely wide attentions from the researchers in various disciplines, such as computer science, social science, biology, economics, electrical engineering, and physics. Network analysis is the study of the network topology to answer a variety of application-based questions regarding the original real world problem. For example in social network analysis the questions are related to how people interact with each other in online social networks, or in collaboration networks, how diseases propagate or how information flows through a network, or how to control a disease or food outbreak. In electric networks like power grids or in internet networks, the questions can be related to vulnerability assessment of the networks to be prepared for power outage or internet blackout. In biological network analysis, the questions are related to how different diseases are related to each other, which can be useful in discovering new symptoms of diseases and producing and developing new medicines. It appears clearly that the reason of the importance of this interdisciplinary area of science, is due to its widespread applications which involves scientists and researchers with a variety of background and interests.

Although networks are much simpler compared to the original complex systems, the interactions among the nodes in the real-world network may seem random, and capturing patterns on these entities is not trivial. There are tremendous questions about inference on networks, which makes this topic very attractive for researchers in the field. In this dissertation we answer some of the questions regarding this topic in two lines of study: one focused on experimental analyses and one focused on theoretical limitations.

In Chapter 2 we look at community detection, a common graph mining task in network inference, which seeks an unsupervised decomposition of a network into groups based on statistical regularities in network connectivity. Although many such algorithms exist, community detection’s No Free Lunch theorem implies that no algorithm can be optimal across all inputs. However, little is known in practice about how different algorithms over or underfit to real networks, or how to reliably assess such behavior across algorithms. We present a broad investigation of over and underfitting across 16 state-of-the-art community detection algorithms applied to a novel benchmark corpus of 572 structurally diverse real-world networks. We find that (i) algorithms vary widely in the number and composition of communities they find, given the same input; (ii) algorithms can be clustered into distinct high-level groups based on similarities of their outputs on real-world networks; (iii) algorithmic differences induce wide variation in accuracy on link-based learning tasks; and, (iv) no algorithm is always the best at such tasks across all inputs. Finally, we quantify each algorithm’s overall tendency to over or underfit to network data using a theoretically principled diagnostic, and discuss the implications for future advances in community detection.

In Chapter 3 we investigate link prediction problem, another important inference task in complex networks with a wide variety of applications. As we observed in Chapter 2, the community detection algorithmic differences induce wide variation in accuracy on link prediction tasks. On the other hand, many link prediction techniques exist in literature and still there is lack of methodology to analyze and compare these techniques. In Chapter 3, we provide a methodological overview of link prediction techniques and present new results on optimal link prediction and on transfer learning for link prediction. In the former, we investigat

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