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A new methodology for model determination in decomposable graphical Gaussian models is developed. The Bayesian paradigm is used and, for each given graph, a hyper inverse Wishart prior distribution on the covariance matrix is considered.…

We introduce efficient Markov chain Monte Carlo methods for inference and model determination in multivariate and matrix-variate Gaussian graphical models. Our framework is based on the G-Wishart prior for the precision matrix associated…

We give methods for Bayesian inference of directed acyclic graphs, DAGs, and the induced causal effects from passively observed complete data. Our methods build on a recent Markov chain Monte Carlo scheme for learning Bayesian networks,…

The forecasting of multi-variate time processes through graph-based techniques has recently been addressed under the graph signal processing framework. However, problems in the representation and the processing arise when each time series…

Graphical models are widely used to make inferences concerning interplay in multivariate systems. In many applications, data are collected from multiple related but nonidentical units whose underlying networks may differ but are likely to…

We consider a graphical model where a multivariate normal vector is associated with each node of the underlying graph and estimate the graphical structure. We minimize a loss function obtained by regressing the vector at each node on those…

We propose autoregressive Bayesian semi-parametric models for waiting times between recurrent events. The aim is two-fold: inference on the effect of possibly time-varying covariates on the gap times and clustering of individuals based on…

Multi-relational networks among entities are frequently observed in the era of big data. Quantifying the effects of multiple networks have attracted significant research interest recently. In this work, we model multiple network effects…

Network growth processes can be understood as generative models of the structure and history of complex networks. This point of view naturally leads to the problem of network archaeology: reconstructing all the past states of a network from…

Graphs are an intuitive way to represent relationships between variables in fields such as finance and neuroscience. However, these graphs often need to be inferred from data. In this paper, we propose a novel framework to infer a latent…

Posterior sampling is a task of central importance in Bayesian inference. For many applications in Bayesian meta-analysis and Bayesian transfer learning, the prior distribution is unknown and needs to be estimated from samples. In practice,…

Graph-based collaborative filtering methods have prevailing performance for recommender systems since they can capture high-order information between users and items, in which the graphs are constructed from the observed user-item…

Acyclic digraphs are the underlying representation of Bayesian networks, a widely used class of probabilistic graphical models. Learning the underlying graph from data is a way of gaining insights about the structural properties of a…

In many applications, data often arise from multiple groups that may share similar characteristics. A joint estimation method that models several groups simultaneously can be more efficient than estimating parameters in each group…

Bayesian Generative AI (BayesGen-AI) methods are developed and applied to Bayesian computation. BayesGen-AI reconstructs the posterior distribution by directly modeling the parameter of interest as a mapping (a.k.a. deep learner) from a…

This paper introduces sparse dynamic chain graph models for network inference in high dimensional non-Gaussian time series data. The proposed method parametrized by a precision matrix that encodes the intra time-slice conditional…

We develop a Bayesian graphical modeling framework for functional data for correlated multivariate random variables observed over a continuous domain. Our method leads to graphical Markov models for functional data which allows the graphs…

We propose a factor network autoregressive (FNAR) model for time series with complex network structures. The coefficients of the model reflect many different types of connections between economic agents ("multilayer network"), which are…

Queue networks describe complex stochastic systems of both theoretical and practical interest. They provide the means to assess alterations, diagnose poor performance and evaluate robustness across sets of interconnected resources. In the…

Graph convolutional neural networks (GCNN) have been successfully applied to many different graph based learning tasks including node and graph classification, matrix completion, and learning of node embeddings. Despite their impressive…