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Probabilistic graphical models that encode an underlying Markov random field are fundamental building blocks of generative modeling to learn latent representations in modern multivariate data sets with complex dependency structures. Among…
We present an objective Bayes method for covariance selection in Gaussian multivariate regression models whose error term has a covariance structure which is Markov with respect to a Directed Acyclic Graph (DAG). The scope is…
Neighborhood selection is a widely used method used for estimating the support set of sparse precision matrices, which helps determine the conditional dependence structure in undirected graphical models. However, reporting only point…
Gaussian conditional random fields (GCRF) are a well-known used structured model for continuous outputs that uses multiple unstructured predictors to form its features and at the same time exploits dependence structure among outputs, which…
We develop Bayesian predictive stacking for geostatistical models, where the primary inferential objective is to provide inference on the latent spatial random field and conduct spatial predictions at arbitrary locations. We exploit…
We propose a mixed integer programming (MIP) model and iterative algorithms based on topological orders to solve optimization problems with acyclic constraints on a directed graph. The proposed MIP model has a significantly lower number of…
A conditional independence graph is a concise representation of pairwise conditional independence among many variables. Graphical Random Forests (GRaFo) are a novel method for estimating pairwise conditional independence relationships among…
We introduce a novel class of graphical models, termed profile graphical models, that represent, within a single graph, how an external factor influences the dependence structure of a multivariate set of variables. This class is quite…
Inspired by the combination of feedforward and iterative computations in the virtual cortex, and taking advantage of the ability of denoising autoencoders to estimate the score of a joint distribution, we propose a novel approach to…
The chain graph model admits both undirected and directed edges in one graph, where symmetric conditional dependencies are encoded via undirected edges and asymmetric causal relations are encoded via directed edges. Though frequently…
Bayesian nonparametric mixtures and random partition models are powerful tools for probabilistic clustering. However, standard independent mixture models can be restrictive in some applications such as inference on cell lineage due to the…
We consider the use of Bayesian information criteria for selection of the graph underlying an Ising model. In an Ising model, the full conditional distributions of each variable form logistic regression models, and variable selection…
Graphical models describe associations between variables through the notion of conditional independence. Gaussian graphical models are a widely used class of such models where the relationships are formalized by non-null entries of the…
We consider the problem of inferring the conditional independence graph (CIG) of a multivariate stationary dicrete-time Gaussian random process based on a finite length observation. Using information-theoretic methods, we derive a lower…
This paper deals with the following problem: modify a Bayesian network to satisfy a given set of probability constraints by only change its conditional probability tables, and the probability distribution of the resulting network should be…
Many algorithms and applications involve repeatedly solving variations of the same inference problem; for example we may want to introduce new evidence to the model or perform updates to conditional dependencies. The goal of adaptive…
Gaussian graphical models are used for determining conditional relationships between variables. This is accomplished by identifying off-diagonal elements in the inverse-covariance matrix that are non-zero. When the ratio of variables (p) to…
Deriving Bayesian inference for exponential random graph models (ERGMs) is a challenging "doubly intractable" problem as the normalizing constants of the likelihood and posterior density are both intractable. Markov chain Monte Carlo (MCMC)…
Complex dynamic systems can be investigated by fitting mechanistic stochastic dynamic models to time series data. In this context, commonly used Monte Carlo inference procedures for model selection and parameter estimation quickly become…
Bayesian inference for graphical models has received much attention in the literature in recent years. It is well known that when the graph G is decomposable, Bayesian inference is significantly more tractable than in the general…