Most real-world networks evolve over time. Existing literature proposes models for dynamic networks that are either unlabeled or assumed to have a single membership structure. On the other hand, a new family of Mixed Membership Stochastic Block Models (MMSBM) allows to model static labeled networks under the assumption of mixed-membership clustering. In this work, we propose to extend this later class of models to infer dynamic labeled networks under a mixed membership assumption. Our approach takes the form of a temporal prior on the model's parameters. It relies on the single assumption that dynamics are not abrupt. We show that our method significantly differs from existing approaches, and allows to model more complex systems --dynamic labeled networks. We demonstrate the robustness of our method with several experiments on both synthetic and real-world datasets. A key interest of our approach is that it needs very few training data to yield good results. The performance gain under challenging conditions broadens the variety of possible applications of automated learning tools --as in social sciences, which comprise many fields where small datasets are a major obstacle to the introduction of machine learning methods.

Last years have seen a regain of interest for the use of stochastic block modeling (SBM) in recommender systems. These models are seen as a flexible alternative to tensor decomposition techniques that are able to handle labeled data. Recent works proposed to tackle discrete recommendation problems via SBMs by considering larger contexts as input data and by adding second order interactions between contexts’ related elements. In this work, we show that these models are all special cases of a single global framework: the Serialized Interacting Mixed membership Stochastic Block Model (SIMSBM). It allows to model an arbitrarily large context as well as an arbitrarily high order of interactions. We demonstrate that SIMSBM generalizes several recent SBM-based baselines. Besides, we demonstrate that our formulation allows for an increased predictive power on five real-world datasets.1

The textual content of a document and its publication date are intertwined. For example, the publication of a news article on a topic is influenced by previous publications on similar issues, according to underlying temporal dynamics. However, it can be challenging to retrieve meaningful information when textual information conveys little information or when temporal dynamics are hard to unveil. Furthermore, the textual content of a document is not always linked to its temporal dynamics. We develop a flexible method to create clusters of textual documents according to both their content and publication time, the Powered Dirichlet-Hawkes process (PDHP). We show PDHP yields significantly better results than state-of-the-art models when temporal information or textual content is weakly informative. The PDHP also alleviates the hypothesis that textual content and temporal dynamics are always perfectly correlated. PDHP allows retrieving textual clusters, temporal clusters, or a mixture of both with high accuracy when they are not. We demonstrate that PDHP generalizes previous work –such as the Dirichlet-Hawkes process (DHP) and Uniform process (UP). Finally, we illustrate the changes induced by PDHP over DHP and UP in a real-world application using Reddit data.

In most real-world applications, it is seldom the case that a result appears independently from an environment. In social networks, users’ behavior results from the people they interact with, news in their feed, or trending topics. In natural language, the meaning of phrases emerges from the combination of words. In general medicine, a diagnosis is established on the basis of the interaction of symptoms. Here, we propose the Interacting Mixed Membership Stochastic Block Model (IMMSBM), which investigates the role of interactions between entities (hashtags, words, memes, etc.) and quantifies their importance within the aforementioned corpora. We find that in inference tasks, taking them into account leads to average relative changes with respect to non-interacting models of up to 150% in the probability of an outcome and greatly improves the predictions performances. Furthermore, their role greatly improves the predictive power of the model. Our findings suggest that neglecting interactions when modeling real-world phenomena might lead to incorrect conclusions being drawn.