Network Models with Alternative Sampling Methods

Networks are an incredible tool to model complex, dependent data and recover insights otherwise hidden. As data engineering technology advances, the abundance and complexity of data skyrocket. The investigation of the relationship between entities in a system sparks rising interest, such as social networks, citation networks, and neural systems, to name a few. Motivated by the demand, numerous network models have been proposed and proven to be adaptive to various scenarios. Yet, models are not the only concern. The sampling mechanism plays a crucial role in truly understanding data. While modeling is mainly about describing data generation, properly recognising how data is observed is just as important. It is not an exaggeration to say that if the sampling mechanism is misspecified, a model is fundamentally inaccurate to the truth. In my two projects, we study data obtained under two specific sampling mechanisms and present models and their theoretical properties tailored to these situations. Egocentric sampling is the backbone of Chapter 2. This sampling design assumes that only a subset of the entities in the community and interactions involving at least one of them are observed. It is designed to resemble the data collection process of social networks. As data privacy is gaining emphasis, we believe that this sampling setting will gain increasing usage. We show that our model excels in both simulation study and real networks compared to benchmarking methods, and present theoretical guarantees on the accuracy of our predictions. Interaction hypergraphs in Chapter 3 are inspired by edge-exchangeable sampling. Contrary to the common assumption that entities are the sampling units, our model assumes that edges are the sampling units instead. Such preference is motivated by real-life networks, such as brain connectivity networks that observe synapses instead of neurons, email networks that observe emails instead of users, and so on. The difference in assumption will result in different probability distributions and require separate modeling strategies. Furthermore, instead of requiring edges to involve only 2 nodes, hypergraphs allow interactions to involve more than 2 nodes and occur multiple times with the same set of nodes. Even though high-degree interactions can be reduced to edges of all the pairs of nodes involved, they are still conceptually different, which we will illustrate below. Finally, we present the theoretical properties and evaluate the clustering performance of our method.