Related papers: Optimal scaling and diffusion limits for the Lange…
We consider the problem of sampling from a distribution governed by a potential function. This work proposes an explicit score based MCMC method that is deterministic, resulting in a deterministic evolution for particles rather than a…
The ability to generate samples of the random effects from their conditional distributions is fundamental for inference in mixed effects models. Random walk Metropolis is widely used to conduct such sampling, but such a method can converge…
Bayesian methods of sampling from a posterior distribution are becoming increasingly popular due to their ability to precisely display the uncertainty of a model fit. Classical methods based on iterative random sampling and posterior…
We develop new flexible univariate models for light-tailed and heavy-tailed data, which extend a hierarchical representation of the generalized Pareto (GP) limit for threshold exceedances. These models can accommodate departure from…
In this paper, we introduce a new approach for integrating score-based models with the Metropolis-Hastings algorithm. While traditional score-based diffusion models excel in accurately learning the score function from data points, they lack…
We propose an algorithm for the efficient and robust sampling of the posterior probability distribution in Bayesian inference problems. The algorithm combines the local search capabilities of the Manifold Metropolis Adjusted Langevin…
It is well known that adding any skew symmetric matrix to the gradient of Langevin dynamics algorithm results in a non-reversible diffusion with improved convergence rate. This paper presents a gradient algorithm to adaptively optimize the…
The Metropolis-Hastings algorithm has been extensively studied in the estimation and simulation literature, with most prior work focusing on convergence behavior and asymptotic theory. However, its covariance structure-an important…
Markov Chain Monte Carlo methods are widely used in signal processing and communications for statistical inference and stochastic optimization. In this work, we introduce an efficient adaptive Metropolis-Hastings algorithm to draw samples…
We analyse computational efficiency of Metropolis-Hastings algorithms with AR(1) process proposals. These proposals include, as a subclass, discretized Langevin diffusion (e.g. MALA) and discretized Hamiltonian dynamics (e.g. HMC). By…
The technique of modifying the geometry of a problem from Euclidean to Hessian metric has proved to be quite effective in optimization, and has been the subject of study for sampling. The Mirror Langevin Diffusion (MLD) is a sampling…
Purpose: The Unadjusted Langevin Algorithm (ULA) in combination with diffusion models can generate high quality MRI reconstructions with uncertainty estimation from highly undersampled k-space data. However, sampling methods such as…
Diffusion models have gained traction as powerful algorithms for synthesizing high-quality images. Central to these algorithms is the diffusion process, a set of equations which maps data to noise in a way that can significantly affect…
NMR is a tool of choice for the measure of diffusion coefficients of species in solution. The DOSY experiment, a 2D implementation of this measure, has proven to be particularly useful for the study of complex mixtures, molecular…
We develop a novel class of MCMC algorithms based on a stochastized Nesterov scheme. With an appropriate addition of noise, the result is a time-inhomogeneous underdamped Langevin equation, which we prove emits a specified target…
Markov chains and diffusion processes are indispensable tools in machine learning and statistics that are used for inference, sampling, and modeling. With the growth of large-scale datasets, the computational cost associated with simulating…
A canonical algorithm for log-concave sampling is the Langevin Algorithm, aka the Langevin Diffusion run with some discretization stepsize $\eta > 0$. This discretization leads the Langevin Algorithm to have a stationary distribution…
We introduce a novel and scalable Bayesian framework for multivariate-density-density regression (DDR), designed to model relationships between multivariate distributions. Our approach addresses the critical issue of distributions residing…
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…
Latent variable models are widely used in social and behavioural sciences, including education, psychology, and political science. With the increasing availability of large and complex datasets, high-dimensional latent variable models have…