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We study nonparametric methods for the setting where multiple distinct networks are observed on the same set of nodes. Such samples may arise in the form of replicated networks drawn from a common distribution, or in the form of…

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…

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…

To learn (statistical) dependencies among random variables requires exponentially large sample size in the number of observed random variables if any arbitrary joint probability distribution can occur. We consider the case that sparse data…

Network analysis has played a key role in knowledge discovery and data mining. In many real-world applications in recent years, we are interested in mining multilayer networks, where we have a number of edge sets called layers, which encode…

We consider the problem of modeling multivariate time series with parsimonious dynamical models which can be represented as sparse dynamic Bayesian networks with few latent nodes. This structure translates into a sparse plus low rank model.…

Graph learning problems are typically approached by focusing on learning the topology of a single graph when signals from all nodes are available. However, many contemporary setups involve multiple related networks and, moreover, it is…

Directed networks are conveniently represented as graphs in which ordered edges encode interactions between vertices. Despite their wide availability, there is a shortage of statistical models amenable for inference, specially when…

We propose to learn latent graphical models when data have mixed variables and missing values. This model could be used for further data analysis, including regression, classification, ranking etc. It also could be used for imputing missing…

We provide the first information theoretic tight analysis for inference of latent community structure given a sparse graph along with high dimensional node covariates, correlated with the same latent communities. Our work bridges recent…

Motivated by distributed machine learning settings such as Federated Learning, we consider the problem of fitting a statistical model across a distributed collection of heterogeneous data sets whose similarity structure is encoded by a…

Large real-world graphs tend to be sparse, but they often contain many densely connected subgraphs and exhibit high clustering coefficients. While recent random graph models can capture this sparsity, they ignore the local density, or vice…

In multivariate statistics, the question of finding direct interactions can be formulated as a problem of network inference - or network reconstruction - for which the Gaussian graphical model (GGM) provides a canonical framework.…

In this paper, we focus on learning sparse graphs with a core-periphery structure. We propose a generative model for data associated with core-periphery structured networks to model the dependence of node attributes on core scores of the…

This paper introduces a new methodology to analyse bipartite and unipartite networks with nonnegative edge values. The proposed approach combines and adapts a number of ideas from the literature on latent variable network models. The…

Random graph models have played a dominant role in the theoretical study of networked systems. The Poisson random graph of Erdos and Renyi, in particular, as well as the so-called configuration model, have served as the starting point for…

We develop novel hierarchical reciprocal graphical models to infer gene networks from heterogeneous data. In the case of data that can be naturally divided into known groups, we propose to connect graphs by introducing a hierarchical prior…

Statistical inference using pairwise comparison data is an effective approach to analyzing large-scale sparse networks. In this paper, we propose a general framework to model the mutual interactions in a network, which enjoys ample…

Much of social network analysis is - implicitly or explicitly - predicated on the assumption that individuals tend to be more similar to their friends than to strangers. Thus, an observed social network provides a noisy signal about the…

Natural physical, chemical, and biological dynamical systems are often complex, with heterogeneous components interacting in diverse ways. We show how simple graph neural networks can be designed to jointly learn the interaction rules and…