The widespread study of networks in diverse domains, including social, technological, and scientific settings, has increased the interest in statistical and machine learning techniques for network analysis. Many of these networks are complex, involving more than one kind of entity, and multiple relationship types, both changing over time. While there have been many network analysis methods proposed for problems such as network evolution, community detection, information diffusion and opinion leader identification, the majority of these methods assume a single entity type, a single edge type and often no temporal dynamics. One of the main shortcomings of these traditional techniques is their inadequacy for capturing higher-order dependencies often present in real, complex networks.

To address these shortcomings, I focus on analysis and inference in dynamic, multi-modal, multi-relational networks, containing multiple entity types (such as people, social groups, organizations, locations, etc.), and different relationship types (such as friendship, membership, affiliation, etc.). An example from social network theory is a network describing users, organizations and interest groups, where users have different types of ties among each other, such as friendship, family ties, etc., as well as affiliation and membership links with organizations and interest groups. By considering the complex structure of these networks rather than limiting the analysis to a single entity or relationship type, I show how we can build richer predictive models that provide better understanding of the network dynamics, and thus result in better quality predictions.

In the first part of my dissertation, I address the problems of network evolution and clustering. For network evolution, I describe methods for modeling the interactions between different modalities, and propose a co-evolution model for social and affiliation networks. I then move to the problem of network clustering, where I propose a novel algorithm for clustering multi-modal, multi-relational data. The second part of my dissertation focuses on the temporal dynamics of interactions in complex networks, from both user-level and network-level perspectives. For the user-centric approach, I analyze the dynamics of user relationships with other entity types, proposing a measure of the "loyalty" a user shows for a given group or topic, based on her temporal interaction pattern. I then move to macroscopic-level approaches for analyzing the dynamic processes that occur on a network scale. I propose a new differential adaptive diffusion model for incorporating diversity and trust in the process of information diffusion on multi-modal, multi-relational networks. I also discuss the implications of the proposed diffusion model on designing new strategies for viral marketing and influential detection. I validate all the proposed methods on several real-world networks from multiple domains.