Related papers: Bayesian model selection for unsupervised image de…
In order to solve tasks like uncertainty quantification or hypothesis tests in Bayesian imaging inverse problems, we often have to draw samples from the arising posterior distribution. For the usually log-concave but high-dimensional…
Graphical models describe associations between variables through the notion of conditional independence. Gaussian graphical models are a widely used class of such models where the relationships are formalized by non-null entries of the…
We consider Bayesian inference in inverse regression problems where the objective is to infer about unobserved covariates from observed responses and covariates. We establish posterior consistency of such unobserved covariates in Bayesian…
Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to…
In Gaussian graphical models, the likelihood equations must typically be solved iteratively. We investigate two algorithms: A version of iterative proportional scaling which avoids inversion of large matrices, and an algorithm based on…
We develop a Bayesian approach for selecting the model which is the most supported by the data within a class of marginal models for categorical variables formulated through equality and/or inequality constraints on generalised logits…
Gaussian graphical models are widely used to infer dependence structures. Bayesian methods are appealing to quantify uncertainty associated with structural learning, i.e., the plausibility of conditional independence statements given the…
We propose a novel framework for joint magnetic resonance image reconstruction and uncertainty quantification using under-sampled k-space measurements. The problem is formulated as a Bayesian linear inverse problem, where prior…
The formulation of Bayesian inverse problems involves choosing prior distributions; choices that seem equally reasonable may lead to significantly different conclusions. We develop a computational approach to better understand the impact of…
Bayesian field theory denotes a nonparametric Bayesian approach for learning functions from observational data. Based on the principles of Bayesian statistics, a particular Bayesian field theory is defined by combining two models: a…
Generative diffusion models can provide powerful prior probability models for inverse problems in imaging, but existing implementations suffer from two key limitations: $(i)$ the prior density is represented implicitly, and $(ii)$ they rely…
A fully Bayesian approach is proposed for ultrahigh-dimensional nonparametric additive models in which the number of additive components may be larger than the sample size, though ideally the true model is believed to include only a small…
We study system design problems stated as parameterized stochastic programs with a chance-constraint set. We adopt a Bayesian approach that requires the computation of a posterior predictive integral which is usually intractable. In…
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 introduce a Bayesian framework for inference with a supervised version of the Gaussian process latent variable model. The framework overcomes the high correlations between latent variables and hyperparameters by using an unbiased pseudo…
Tomographic reconstruction, despite its revolutionary impact on a wide range of applications, suffers from its ill-posed nature in that there is no unique solution because of limited and noisy measurements. Therefore, in the absence of…
In this paper we propose a new Bayesian estimation method to solve linear inverse problems in signal and image restoration and reconstruction problems which has the property to be scale invariant. In general, Bayesian estimators are {\em…
This paper presents a novel stochastic optimisation methodology to perform empirical Bayesian inference in semi-blind image deconvolution problems. Given a blurred image and a parametric class of possible operators, the proposed…
This paper analyzes hierarchical Bayesian inverse problems using techniques from high-dimensional statistics. Our analysis leverages a property of hierarchical Bayesian regularizers that we call approximate decomposability to obtain…
We consider an acoustic obstacle reconstruction problem with Poisson data. Due to the stochastic nature of the data, we tackle this problem in the framework of Bayesian inversion. The unknown obstacle is parameterized in its angular form.…