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We introduce a framework that enables efficient sampling from learned probability distributions for MRI reconstruction. Different from conventional deep learning-based MRI reconstruction techniques, samples are drawn from the posterior…
Modern cosmological analyses constrain physical parameters using Markov Chain Monte Carlo (MCMC) or similar sampling techniques. Oftentimes, these techniques are computationally expensive to run and require up to thousands of CPU hours to…
We propose a Bayesian nonparametric mixture model for the reconstruction and prediction from observed time series data, of discretized stochastic dynamical systems, based on Markov Chain Monte Carlo methods (MCMC). Our results can be used…
Developing efficient Bayesian computation algorithms for imaging inverse problems is challenging due to the dimensionality involved and because Bayesian imaging models are often not smooth. Current state-of-the-art methods often address…
Graph-based machine learning has seen an increased interest over the last decade with many connections to other fields of applied mathematics. Learning based on partial differential equations, such as the phase-field Allen-Cahn equation,…
High-throughput characterization often requires estimating parameters and model dimension from experimental data of limited quantity and quality. Such data may result in an ill-posed inverse problem, where multiple sets of parameters and…
This paper presents a new approach to automatically discovering accurate models of complex time series data. Working within a Bayesian nonparametric prior over a symbolic space of Gaussian process time series models, we present a novel…
Learning a Bayesian network (BN) from data can be useful for decision-making or discovering causal relationships. However, traditional methods often fail in modern applications, which exhibit a larger number of observed variables than data…
Bayesian estimation of Gaussian graphical models has proven to be challenging because the conjugate prior distribution on the Gaussian precision matrix, the G-Wishart distribution, has a doubly intractable partition function. Recent…
The Bayesian approach to Inverse Problems relies predominantly on Markov Chain Monte Carlo methods for posterior inference. The typical nonlinear concentration of posterior measure observed in many such Inverse Problems presents severe…
Bayesian inverse problems are often computationally challenging when the forward model is governed by complex partial differential equations (PDEs). This is typically caused by expensive forward model evaluations and high-dimensional…
The use of Cauchy Markov random field priors in statistical inverse problems can potentially lead to posterior distributions which are non-Gaussian, high-dimensional, multimodal and heavy-tailed. In order to use such priors successfully,…
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…
Gaussian approximations are routinely employed in Bayesian statistics to ease inference when the target posterior is intractable. Although these approximations are asymptotically justified by Bernstein-von Mises type results, in practice…
Sequential optimization methods are often confronted with the curse of dimensionality in high-dimensional spaces. Current approaches under the Gaussian process framework are still burdened by the computational complexity of tracking…
Posterior sampling by Monte Carlo methods provides a more comprehensive solution approach to inverse problems than computing point estimates such as the maximum posterior using optimization methods, at the expense of usually requiring many…
Monte Carlo (MC) generators are crucial for analyzing data in particle collider experiments. However, often even a small mismatch between the MC simulations and the measurements can undermine the interpretation of the results. This is…
We construct a new framework for accelerating Markov chain Monte Carlo in posterior sampling problems where standard methods are limited by the computational cost of the likelihood, or of numerical models embedded therein. Our approach…
We present a new Markov chain Monte Carlo method for estimating posterior probabilities of structural features in Bayesian networks. The method draws samples from the posterior distribution of partial orders on the nodes; for each sampled…
This paper considers the objective comparison of stochastic models to solve inverse problems, more specifically image restoration. Most often, model comparison is addressed in a supervised manner, that can be time-consuming and partly…