Related papers: Learning Markov Network Structure using Brownian D…
Gaussian graphical models are a popular tool to learn the dependence structure in the form of a graph among variables of interest. Bayesian methods have gained in popularity in the last two decades due to their ability to simultaneously…
Information theoretic measures (e.g. the Kullback Liebler divergence and Shannon mutual information) have been used for exploring possibly nonlinear multivariate dependencies in high dimension. If these dependencies are assumed to follow a…
Although multivariate count data are routinely collected in many application areas, there is surprisingly little work developing flexible models for characterizing their dependence structure. This is particularly true when interest focuses…
A fundamental method of reconstructing networks, e.g. in the context of gene regulation, relies on the precision matrix (the inverse of the variance-covariance matrix) as an indicator which variables are associated with each other. The…
We propose a novel Bayesian methodology which uses random walks for rapid inference of statistical properties of undirected networks with weighted or unweighted edges. Our formalism yields high-accuracy estimates of the probability…
Graphical model learning and inference are often performed using Bayesian techniques. In particular, learning is usually performed in two separate steps. First, the graph structure is learned from the data; then the parameters of the model…
Given partial measurements of a time-varying graph signal, we propose an algorithm to simultaneously estimate both the underlying graph topology and the missing measurements. The proposed algorithm operates by training an interpretable…
Network data arises through observation of relational information between a collection of entities. Recent work in the literature has independently considered when (i) one observes a sample of networks, connectome data in neuroscience being…
Mixed data refers to a type of data in which variables can be of multiple types, such as continuous, discrete, or categorical. This data is routinely collected in various fields, including healthcare and social sciences. A common goal in…
Deep Learning's recent successes have mostly relied on Convolutional Networks, which exploit fundamental statistical properties of images, sounds and video data: the local stationarity and multi-scale compositional structure, that allows…
Undirected graphs are often used to describe high dimensional distributions. Under sparsity conditions, the graph can be estimated using $\ell_1$ penalization methods. However, current methods assume that the data are independent and…
Undirected graphs can be used to describe matrix variate distributions. In this paper, we develop new methods for estimating the graphical structures and underlying parameters, namely, the row and column covariance and inverse covariance…
In the process of building (structural learning) a probabilistic graphical model from a set of observed data, the directional, cyclic dependencies between the random variables of the model are often found. Existing graphical models such as…
This paper considers learning of the graphical structure of a $p$-dimensional random vector $X \in R^p$ using both parametric and non-parametric methods. Unlike the previous works which observe $x$ directly, we consider the indirect…
We present two algorithms for learning the structure of a Markov network from data: GSMN* and GSIMN. Both algorithms use statistical independence tests to infer the structure by successively constraining the set of structures consistent…
Feature learning in the presence of a mixed type of variables, numerical and categorical types, is an important issue for related modeling problems. For simple neighborhood queries under mixed data space, standard practice is to consider…
In this article a novel approach for training deep neural networks using Bayesian techniques is presented. The Bayesian methodology allows for an easy evaluation of model uncertainty and additionally is robust to overfitting. These are…
Identifying a coupled dynamical system out of many plausible candidates, each of which could serve as the underlying generator of some observed measurements, is a profoundly ill posed problem that commonly arises when modelling real world…
We discuss probabilistic models of random covariance structures defined by distributions over sparse eigenmatrices. The decomposition of orthogonal matrices in terms of Givens rotations defines a natural, interpretable framework for…
We address the problem of Bayesian structure learning for domains with hundreds of variables by employing non-parametric bootstrap, recursively. We propose a method that covers both model averaging and model selection in the same framework.…