We consider the problem of learning the structure of a pairwise graphical model over continuous and discrete variables. We present a new pairwise model for graphical models with both continuous and discrete variables that is amenable to structure learning. In previous work, authors have considered structure learning of Gaussian graphical models and structure learning of discrete models. Our app...

Functional models are frequently used in computer vision and photogrammetry, as they enable the mathematical formulation of several problems such as pose computation and more generally the parameter estimation problem. However, the structural properties of such models have only seldom been studied. This contribution is dedicated to the analysis of such properties. We propose a new formalism tha...

Undirected graphical models, such as Gaussian graphical models, Ising, and multinomial/categorical graphical models, are widely used in a variety of applications for modeling distributions over a large number of variables. These standard instances, however, are ill-suited to modeling count data, which are increasingly ubiquitous in big-data settings such as genomic sequencing data, user-ratings...

Markov chain Monte Carlo techniques have revolutionized the field of Bayesian statistics. Their enormous power and their generalizability have rendered them the method of choice for statistical inference in many scientific disciplines. Their power is so great that they can even accommodate situations in which the structure of the statistical model itself is uncertain. However, the analysis of s...

Matrix-variate observations are frequently encountered in many contemporary statistical problems due to a rising need to organize and analyze data with structured information. In this paper, we propose a novel sparse matrix graphical model for this type of statistical problems. By penalizing respectively two precision matrices corresponding to the rows and columns, our method yields a sparse ma...

In this chapter we propose a modification of CRF-like algorithms that allows for solving large-scale structured classification problems. Our approach consists in upper bounding the CRF functional in order to decompose its training into independent optimisation problems per clique. Furthermore we show that each sub-problem corresponds to solving a multiclass learning task in each clique, which e...

“Graphical models” combine graph theory and probability theory to provide a general framework for representing models in which a number of variables interact. Graphical models trace their origins to many different fields and have been applied in wide variety of settings: for example, to develop probabilistic expert systems, to understand neural network models, to infer trait inheritance in gene...

We propose a comprehensive Bayesian approach for graphical model determination in observational studies that can accommodate binary, ordinal or continuous variables simultaneously. Our new models are called copula Gaussian graphical models and embed graphical model selection inside a semiparametric Gaussian copula. The domain of applicability of our methods is very broad and encompass many stud...