Related papers: Posterior convergence rates for estimating large p…
We propose a Bayesian approximate inference method for learning the dependence structure of a Gaussian graphical model. Using pseudo-likelihood, we derive an analytical expression to approximate the marginal likelihood for an arbitrary…
In a traditional Gaussian graphical model, data homogeneity is routinely assumed with no extra variables affecting the conditional independence. In modern genomic datasets, there is an abundance of auxiliary information, which often gets…
Maximum a posteriori (MAP) estimation, like all Bayesian methods, depends on prior assumptions. These assumptions are often chosen to promote specific features in the recovered estimate. The form of the chosen prior determines the shape of…
We consider the asymptotic behavior of posterior distributions and Bayes estimators based on observations which are required to be neither independent nor identically distributed. We give general results on the rate of convergence of the…
Sparse Bayesian factor models are routinely implemented for parsimonious dependence modeling and dimensionality reduction in high-dimensional applications. We provide theoretical understanding of such Bayesian procedures in terms of…
In Gaussian graphical models, the zero entries in the precision matrix determine the dependence structure, so estimating that sparse precision matrix and, thereby, learning this underlying structure, is an important and challenging problem.…
A precision matrix is the inverse of a covariance matrix. In this paper, we study the problem of estimating the precision matrix with a known graphical structure under high-dimensional settings. We propose a simple estimator of the…
In Bayesian theory, calculating a posterior probability distribution is highly important but usually difficult. Therefore, some methods have been put forward to deal with such problem, among which, the most popular one is the asymptotic…
Gaussian graphical modeling has been widely used to explore various network structures, such as gene regulatory networks and social networks. We often use a penalized maximum likelihood approach with the $L_1$ penalty for learning a…
We consider the problem of Bayesian causal discovery for the standard model of linear structural equations with equivariant Gaussian noise. A uniform prior is placed on the space of directed acyclic graphs (DAGs) over a fixed set of…
In Bayesian applications, there is a huge interest in rapid and accurate estimation of the posterior distribution, particularly for high dimensional or hierarchical models. In this article, we propose to use optimization to solve for a…
Gaussian time-series models are often specified through their spectral density. Such models present several computational challenges, in particular because of the non-sparse nature of the covariance matrix. We derive a fast approximation of…
Marginal likelihood, also known as model evidence, is a fundamental quantity in Bayesian statistics. It is used for model selection using Bayes factors or for empirical Bayes tuning of prior hyper-parameters. Yet, the calculation of…
Covariance estimation and selection for multivariate datasets in a high-dimensional regime is a fundamental problem in modern statistics. Gaussian graphical models are a popular class of models used for this purpose. Current Bayesian…
This article explores the estimation of precision matrices in high-dimensional Gaussian graphical models. We address the challenge of improving the accuracy of maximum likelihood-based precision estimation through penalization.…
While Bayesian methods are extremely popular in statistics and machine learning, their application to massive datasets is often challenging, when possible at all. Indeed, the classical MCMC algorithms are prohibitively slow when both the…
We explore various Bayesian approaches to estimate partial Gaussian graphical models. Our hierarchical structures enable to deal with single-output as well as multiple-output linear regressions, in small or high dimension, enforcing either…
Estimating conditional independence graphs from high-dimensional Gaussian data is challenging because methods must detect relevant edges while rigorously controlling statistical errors. We propose a Bayesian framework based on a prior…
We consider fully connected and feedforward deep neural networks with dependent and possibly heavy-tailed weights, as introduced in [26], to address limitations of the standard Gaussian prior. It has been proved in [26] that, as the number…
In a modern observational study based on healthcare databases, the number of observations and of predictors typically range in the order of $10^5$ ~ $10^6$ and of $10^4$ ~ $10^5$. Despite the large sample size, data rarely provide…