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Latent representations are the essence of deep generative models and determine their usefulness and power. For latent representations to be useful as generative concept representations, their latent space must support latent space…

Adaptive networks model social, physical, technical, or biological systems as attributed graphs evolving at the level of both their topology and data. They are naturally described by graph transformation, but the majority of authors take an…

Representation learning over graph structured data has been mostly studied in static graph settings while efforts for modeling dynamic graphs are still scant. In this paper, we develop a novel hierarchical variational model that introduces…

We consider the problem of model selection in Gaussian Markov fields in the sample deficient scenario. In many practically important cases, the underlying networks are embedded into Euclidean spaces. Using the natural geometric structure,…

Recent research has shown growing interest in modeling hypergraphs, which capture polyadic interactions among entities beyond traditional dyadic relations. However, most existing methodologies for hypergraphs face significant limitations,…

A broad set of empirical phenomenon in the study of social, economic and machine behaviour can be modelled as complex systems with averaging dynamics. However many of these models naturally result in consensus or consensus-like outcomes. In…

A graphical model is a statistical model that is associated to a graph whose nodes correspond to variables of interest. The edges of the graph reflect allowed conditional dependencies among the variables. Graphical models admit…

Full probability models are critical for the statistical modeling of complex networks, and yet there are few general, flexible and widely applicable generative methods. We propose a new family of probability models motivated by the idea of…

Latent tree analysis seeks to model the correlations among a set of random variables using a tree of latent variables. It was proposed as an improvement to latent class analysis --- a method widely used in social sciences and medicine to…

Graphical Gaussian models have proven to be useful tools for exploring network structures based on multivariate data. Applications to studies of gene expression have generated substantial interest in these models, and resulting recent…

Spectral embedding of adjacency or Laplacian matrices of undirected graphs is a common technique for representing a network in a lower dimensional latent space, with optimal theoretical guarantees. The embedding can be used to estimate the…

As more and more network-structured data sets are available, the statistical analysis of valued graphs has become common place. Looking for a latent structure is one of the many strategies used to better understand the behavior of a…

Significant efforts have gone into the development of statistical models for analyzing data in the form of networks, such as social networks. Most existing work has focused on modeling static networks, which represent either a single time…

We construct a novel class of stochastic blockmodels using Bayesian nonparametric mixtures. These model allows us to jointly estimate the structure of multiple networks and explicitly compare the community structures underlying them, while…

Stochastic frontier models have attracted considerable attention due to the incorporation of an inefficiency term in addition to the conventional error term. In this paper, we propose a general estimation framework for panel stochastic…

We consider a class of growth models and models of turbulence based on the randomly stirred fluid. The similarity between the predictions of these models, noted a decade earlier, is understood on the basis of a stochastic quantization…

Models of complex networks often incorporate node-intrinsic properties abstracted as hidden variables. The probability of connections in the network is then a function of these variables. Real-world networks evolve over time, and many…

A semi-parametric, non-linear regression model in the presence of latent variables is applied towards learning network graph structure. These latent variables can correspond to unmodeled phenomena or unmeasured agents in a complex system of…

The commonly used latent space embedding techniques, such as Principal Component Analysis, Factor Analysis, and manifold learning techniques, are typically used for learning effective representations of homogeneous data. However, they do…

Reciprocity, or the stochastic tendency for actors to form mutual relationships, is an essential characteristic of directed network data. Existing latent space approaches to modeling directed networks are severely limited by the assumption…