Related papers: Bayesian model selection for unsupervised image de…

Matrix completion and robust principal component analysis have been widely used for the recovery of data suffering from missing entries or outliers. In many real-world applications however, the data is also time-varying, and the naive…

A common problem in natural sciences is the comparison of competing models in the light of observed data. Bayesian model comparison provides a statistically sound framework for this comparison based on the evidence each model provides for…

Bayesian models often involve a small set of hyperparameters determined by maximizing the marginal likelihood. Bayesian optimization is a popular iterative method where a Gaussian process posterior of the underlying function is sequentially…

We propose a method to restore and to segment simultaneously images degraded by a known point spread function (PSF) and additive white noise. For this purpose, we propose a joint Bayesian estimation framework, where a family of…

Solving ill-posed inverse problems by Bayesian inference has recently attracted considerable attention. Compared to deterministic approaches, the probabilistic representation of the solution by the posterior distribution can be exploited to…

Score-based diffusion methods provide a powerful strategy to solve image restoration tasks by flexibly combining a pre-trained foundational prior model with a likelihood function specified during test time. Such methods are predominantly…

It has historically been a challenge to perform Bayesian inference in a design-based survey context. The present paper develops a Bayesian model for sampling inference in the presence of inverse-probability weights. We use a hierarchical…

Bayesian model selection, with precedents in George and McCulloch (1993) and Abramovich et al. (1998), support credibility measures that relate model uncertainty, but computation can be costly when sparse priors are approximate. We design…

In solving Bayesian inverse problems, it is often desirable to use a common density parameterization to denote the prior and posterior. Typically we seek a density from the same family as the prior which closely approximates the true…

Uncertainty quantification in image retrieval is crucial for downstream decisions, yet it remains a challenging and largely unexplored problem. Current methods for estimating uncertainties are poorly calibrated, computationally expensive,…

Current causal discovery approaches require restrictive model assumptions in the absence of interventional data to ensure structure identifiability. These assumptions often do not hold in real-world applications leading to a loss of…

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…

Unsupervised image segmentation aims at clustering the set of pixels of an image into spatially homogeneous regions. We introduce here a class of Bayesian nonparametric models to address this problem. These models are based on a combination…

Gaussian graphical models typically assume a homogeneous structure across all subjects, which is often restrictive in applications. In this article, we propose a weighted pseudo-likelihood approach for graphical modeling which allows…

We introduce non-stationary Mat\'ern field priors with stochastic partial differential equations, and construct correlation length-scaling with hyperpriors. We model both the hyperprior and the Mat\'ern prior as continuous-parameter random…

The Bayesian Conjugate Gradient method (BayesCG) is a probabilistic generalization of the Conjugate Gradient method (CG) for solving linear systems with real symmetric positive definite coefficient matrices. Our CG-based implementation of…

We present a non-parametric Bayesian approach to structure learning with hidden causes. Previous Bayesian treatments of this problem define a prior over the number of hidden causes and use algorithms such as reversible jump Markov chain…

Full Bayesian posteriors are rarely analytically tractable, which is why real-world Bayesian inference heavily relies on approximate techniques. Approximations generally differ from the true posterior and require diagnostic tools to assess…

Bayesian learning is built on an assumption that the model space contains a true reflection of the data generating mechanism. This assumption is problematic, particularly in complex data environments. Here we present a Bayesian…

We propose a Bayesian inference framework to estimate uncertainties in inverse scattering problems. Given the observed data, the forward model and their uncertainties, we find the posterior distribution over a finite parameter field…