Adrien Dulac -A study of Mixed-Membership Models for Complex Networks Analysis

Relational data are ubiquitous in the nature and their accessibility has not ceased to increase in recent years. Those data, see as a whole, form a network, which can be represented by a data structure called a graph, where each vertex of the graph is an entity and each edge a connection between pair of vertices. Complex networks in general, such as the Web, communication networks or social network, are known to exhibit common structural properties that emerge through their graphs. In this work we emphasize two important properties called *homophilly* and *preferential attachment* that arise on most of the real-world networks. We firstly study a class of powerful *random graph models* in a Bayesian nonparametric setting, called *mixed-membership model* and we focus on showing whether the models in this class comply with the mentioned properties, after giving formal definitions in a probabilistic context of the latter. Furthermore, we empirically evaluate our findings on synthetic and real-world network datasets. Secondly, we propose a new model, which extends the former Stochastic Mixed-Membership Model, for weighted networks and we develop an efficient inference algorithm able to scale to large-scale networks.