Block-Structure Based Time-Series Models For Graph Sequences

Statistical node clustering in discrete time dynamic networks is an emerging field that raises many challenges. Here, we explore statistical properties and frequentist inference in a model that combines a stochastic block model (SBM) for its static part with independent Markov chains for the evolution of the nodes groups through time. We model binary data as well as weighted dynamic random graphs (with discrete or continuous edges values). Our approach, motivated by the impor...

Temporal Networks, and more specifically, Markovian Temporal Networks, present a unique challenge regarding the community discovery task. The inherent dynamism of these systems requires an intricate understanding of memory effects and structural heterogeneity, which are often key drivers of network evolution. In this study, we address these aspects by introducing an innovative approach to community detection, centered around a novel modularity function. We focus on demonstrat...

The task of \emph{community detection} in a graph formalizes the intuitive task of grouping together subsets of vertices such that vertices within clusters are connected tighter than those in disparate clusters. This paper approaches community detection in graphs by constructing Markov random walks on the graphs. The mixing properties of the random walk are then used to identify communities. We use coupling from the past as an algorithmic primitive to translate the mixing pro...

We present a selective review on probabilistic modeling of heterogeneity in random graphs. We focus on latent space models and more particularly on stochastic block models and their extensions that have undergone major developments in the last five years.

Clustering and community detection with multiple graphs have typically focused on aligned graphs, where there is a mapping between nodes across the graphs (e.g., multi-view, multi-layer, temporal graphs). However, there are numerous application areas with multiple graphs that are only partially aligned, or even unaligned. These graphs are often drawn from the same population, with communities of potentially different sizes that exhibit similar structure. In this paper, we dev...

We propose a nonparametric approach to link prediction in large-scale dynamic networks. Our model uses graph-based features of pairs of nodes as well as those of their local neighborhoods to predict whether those nodes will be linked at each time step. The model allows for different types of evolution in different parts of the graph (e.g, growing or shrinking communities). We focus on large-scale graphs and present an implementation of our model that makes use of locality-sen...

We consider the problem of analyzing timestamped relational events between a set of entities, such as messages between users of an on-line social network. Such data are often analyzed using static or discrete-time network models, which discard a significant amount of information by aggregating events over time to form network snapshots. In this paper, we introduce a block point process model (BPPM) for continuous-time event-based dynamic networks. The BPPM is inspired by the ...

We introduce the Markov Stochastic Block Model (MSBM): a growth model for community based networks where node attributes are assigned through a Markovian dynamic. We rely on HMMs' literature to design prediction methods that are robust to local clustering errors. We focus specifically on the link prediction and collaborative filtering problems and we introduce a new model selection procedure to infer the number of hidden clusters in the network. Our approaches for reliable pr...

This work presents a novel modeling and analysis framework for graph sequences which addresses the challenge of detecting and contextualizing anomalies in labelled, streaming graph data. We introduce a generalization of the BTER model of Seshadhri et al. by adding flexibility to community structure, and use this model to perform multi-scale graph anomaly detection. Specifically, probability models describing coarse subgraphs are built by aggregating probabilities at finer lev...

Neural node embeddings have recently emerged as a powerful representation for supervised learning tasks involving graph-structured data. We leverage this recent advance to develop a novel algorithm for unsupervised community discovery in graphs. Through extensive experimental studies on simulated and real-world data, we demonstrate that the proposed approach consistently improves over the current state-of-the-art. Specifically, our approach empirically attains the information...