Dynamic Relational Models of Complex Network

Abstract

Analysis of complex networks is one of the most important topics in the Machine Learning field. At the same time, classical probabilistic graphical relational models are one of the most popular methods used to perform such tasks. However, there are several limitations associated with a process of constructing probabilistic relational models. Some of them are: inability to cope with fully masked data; assumptions of data independence; insufficient interpretability and precision of models; and inadequate modelling of network's dynamics in continuous time. All this leads to construction of simplified models, as well as lack of full utilization of the available data. In this thesis, we proposed a number of methods developed based on different types of Machine Learning techniques, such as Deep Learning and Bayesian nonparametric and stochastic processes, to address these limitations. More specifically, we propose some modifications of the mixed membership stochastic blockmodel, i.e., we focus on modeling: 1) coupling relations within/across groups/communities of nodes using the multilayer network with static settings; 2) coupling relations between communities using a matrix factorization method; and 3) coupling relations between nodes across groups/communities using a long short term memory. In addition, we also improve the ability of relational models from the perspective of accuracy~(model performance) and interpretability. In this case, we enable clustering of both nodes and edges simultaneously. We use discrete fragmentation coagulation process to cluster nodes of a network, and mixed membership stochastic blockmodel to cluster its edges. Furthermore, we focus on modelling changes in relational data occurring over continuous time. Specifically, in order to prevent an information loss we use the continuous fragmentation coagulation process to model the community evolution, as well as Hawkes process to model the reciprocating relation among nodes. We validate our model using synthetic and real datasets.