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Integrating intelligent systems, such as robots, into dynamic group settings poses challenges due to the mutual influence of human behaviors and internal states. A robust representation of social interaction dynamics is essential for…

The analysis of spatial point patterns that occur in the network domain have recently gained much attraction and various intensity functions and measures have been proposed. However, the linkage of spatial network statistics to regression…

Recently, the classical configuration model for random graphs with given degree distribution has been extensively used as a null model in contraposition to real networks with the same degree distribution. In this paper, we briefly review…

Many real-world networks are intrinsically directed. Such networks include activation of genes, hyperlinks on the internet, and the network of followers on Twitter among many others. The challenge, however, is to create a network model that…

Social recommendations have been widely adopted in substantial domains. Recently, graph neural networks (GNN) have been employed in recommender systems due to their success in graph representation learning. However, dealing with the dynamic…

This manuscript investigates the stochastic comparisons of the second-order statistics from dependent and heterogeneous general semi-parametric family of distributions observations. Some sufficient conditions on the usual stochastic order…

Neural network design has utilized flexible nonlinear processes which can mimic biological systems, but has suffered from a lack of traceability in the resulting network. Graphical probabilistic models ground network design in probabilistic…

Probabilistic independence can dramatically simplify the task of eliciting, representing, and computing with probabilities in large domains. A key technique in achieving these benefits is the idea of graphical modeling. We survey existing…

Dynamic models and statistical inference for the diffusion of information in social networks is an area which has witnessed remarkable progress in the last decade due to the proliferation of social networks. Modeling and inference of…

Empirical networks are often globally sparse, with a small average number of connections per node, when compared to the total size of the network. However, this sparsity tends not to be homogeneous, and networks can also be locally dense,…

Graphical causal models are an important tool for knowledge discovery because they can represent both the causal relations between variables and the multivariate probability distributions over the data. Once learned, causal graphs can be…

The mechanism of preferential attachment underpins most recent social network formation models. Yet few authors attempt to check or quantify assumptions on this mechanism. We call generalized preferential attachment any kind of preference…

This tutorial provides a concise introduction to modern causal modeling by integrating potential outcomes and graphical methods. We motivate causal questions such as counterfactual reasoning under interventions and define binary treatments…

In one-dimensional, heterogeneous systems, the whole traffic dynamics depend strongly on the behavior of the leading vehicle. This result holds for a class of vehicular traffic models satisfying the following properties. The interactions…

We consider a random model for directed graphs whereby an arc is placed from one vertex to another with a prescribed probability which may vary from arc to arc. Using perturbation bounds as well as Chernoff inequalities, we show that the…

Consider stochastic models for the spread of an infection in a structured community, where this structured community is itself described by a random network model. Some common network models and transmission models are defined and large…

Systems which consist of many localized constituents interacting with each other can be represented by complex networks. Consistently, network science has become highly popular in vast fields focusing on natural, artificial and social…

A model for statistical ranking is a family of probability distributions whose states are orderings of a fixed finite set of items. We represent the orderings as maximal chains in a graded poset. The most widely used ranking models are…

Network data often take the form of repeated interactions between senders and receivers tabulated over time. A primary question to ask of such data is which traits and behaviors are predictive of interaction. To answer this question, a…

We investigate the algebra and geometry of general interventions in discrete DAG models. To this end, we introduce a theory for modeling soft interventions in the more general family of staged tree models and develop the formalism to study…