Related papers: Bayesian Regularization of Gaussian Graphical Mode…

The current standard Bayesian approach to model calibration, which assigns a Gaussian process prior to the discrepancy term, often suffers from issues of unidentifiability and computational complexity and instability. When the goal is to…

Structure learning algorithms that learn the graph of a Bayesian network from observational data often do so by assuming the data correctly reflect the true distribution of the variables. However, this assumption does not hold in the…

Bayesian statistics has gained popularity in psychological research due to its intuitive uncertainty quantification and convenient information-updating rules. In many applications, however, prior distributions are introduced merely as…

High-precision measurements require optimal setups and analysis tools to achieve continuous improvements. Systematic corrections need to be modeled with high accuracy and known uncertainty to reconstruct underlying physical phenomena. To…

Bayesian methods for low-rank matrix completion with noise have been shown to be very efficient computationally. While the behaviour of penalized minimization methods is well understood both from the theoretical and computational points of…

We consider the problem of calibrating an imperfect computer model using experimental data. To compensate the misspecification of the computer model and make more accurate predictions, a discrepancy function is often included and modeled…

Gaussian graphical models with sparsity in the inverse covariance matrix are of significant interest in many modern applications. For the problem of recovering the graphical structure, information criteria provide useful optimization…

Gaussian graphical models have been used to study intrinsic dependence among several variables, but the Gaussianity assumption may be restrictive in many applications. A nonparanormal graphical model is a semiparametric generalization for…

We propose two novel approaches to the recovery of an (approximately) sparse signal from noisy linear measurements in the case that the signal is a priori known to be non-negative and obey given linear equality constraints, such as simplex…

We consider the problem of learning a causal graph in the presence of measurement error. This setting is for example common in genomics, where gene expression is corrupted through the measurement process. We develop a provably consistent…

Preferential sampling is a common feature in geostatistics and occurs when the locations to be sampled are chosen based on information about the phenomena under study. In this case, point pattern models are commonly used as the probability…

This paper presents an efficient Bayesian framework for solving nonlinear, high-dimensional model calibration problems. It is based on a Variational Bayesian formulation that aims at approximating the exact posterior by means of solving an…

We develop a method for reconstructing regulatory interconnection networks between variables evolving according to a linear dynamical system. The work is motivated by the problem of gene regulatory network inference, that is, finding causal…

This paper proposes a new approach for Bayesian and maximum likelihood parameter estimation for stationary Gaussian processes observed on a large lattice with missing values. We propose an MCMC approach for Bayesian inference, and a Monte…

In statistical applications, it is common to encounter parameters supported on a varying or unknown dimensional space. Examples include the fused lasso regression, the matrix recovery under an unknown low rank, etc. Despite the ease of…

Regularization is a common tool in variational inverse problems to impose assumptions on the parameters of the problem. One such assumption is sparsity, which is commonly promoted using lasso and total variation-like regularization.…

Modern imaging techniques heavily rely on Bayesian statistical models to address difficult image reconstruction and restoration tasks. This paper addresses the objective evaluation of such models in settings where ground truth is…

Gene regulatory networks play a crucial role in controlling an organism's biological processes, which is why there is significant interest in developing computational methods that are able to extract their structure from high-throughput…

Bayesian model updating based on Gaussian Process (GP) models has received attention in recent years, which incorporates kernel-based GPs to provide enhanced fidelity response predictions. Although most kernel functions provide high fitting…

Variational inference techniques based on inducing variables provide an elegant framework for scalable posterior estimation in Gaussian process (GP) models. Besides enabling scalability, one of their main advantages over sparse…