Related papers: Geodesic Slice Sampler for Multimodal Distribution…
Hamiltonian Monte Carlo (HMC) and its dynamic extensions, such as the No-U-Turn Sampler (NUTS), are powerful Markov chain Monte Carlo methods for sampling from complex, high-dimensional probability distributions. Riemannian manifold…
In many robot motion planning problems, task objectives and physical constraints induce non-Euclidean geometry on the configuration space, yet many planners operate using Euclidean distances that ignore this structure. We address the…
Standard Markov chain Monte Carlo methods struggle to explore distributions that are concentrated in the neighbourhood of low-dimensional structures. These pathologies naturally occur in a number of situations. For example, they are common…
We describe an MCMC method for sampling distributions with soft constraints, which are constraints that are almost but not exactly satisfied. We sample a total distribution that is a convex combination of the target soft distribution with…
Markov Chain Monte Carlo (MCMC) sampling methods are widely used but often encounter either slow convergence or biased sampling when applied to multimodal high dimensional distributions. In this paper, we present a general framework of…
Elliptical slice sampling, when adapted to linearly truncated multivariate normal distributions, is a rejection-free Markov chain Monte Carlo method. At its core, it requires analytically constructing an ellipse-polytope intersection. The…
It is known that the simple slice sampler has robust convergence properties, however the class of problems where it can be implemented is limited. In contrast, we consider hybrid slice samplers which are easily implementable and where…
In this paper, we propose a MCMC algorithm based on elliptical slice sampling with the purpose to improve sampling efficiency. During sampling, a mixture distribution is fitted periodically to previous samples. The components of the mixture…
Markov chain Monte Carlo (MCMC) methods have existed for a long time and the field is well-explored. The purpose of MCMC methods is to approximate a distribution through repeated sampling; most MCMC algorithms exhibit asymptotically optimal…
Science and engineering problems subject to uncertainty are frequently both computationally expensive and feature nonsmooth parameter dependence, making standard Monte Carlo too slow, and excluding efficient use of accelerated uncertainty…
Hamiltonian Monte Carlo is a prominent Markov Chain Monte Carlo algorithm, which employs symplectic integrators to sample from high dimensional target distributions in many applications, such as statistical mechanics, Bayesian statistics…
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…
Markov Chain Monte Carlo (MCMC) methods are a popular technique in Bayesian statistical modeling. They have long been used to obtain samples from posterior distributions, but recent research has focused on the scalability of these…
The Riemannian manifold of curves with a Sobolev metric is an important and frequently studied model in the theory of shape spaces. Various numerical approaches have been proposed to compute geodesics, but so far elude a rigorous…
We consider the problem of sampling from posterior distributions for Bayesian models where some parameters are restricted to be orthogonal matrices. Such matrices are sometimes used in neural networks models for reasons of regularization…
The need to calibrate increasingly complex statistical models requires a persistent effort for further advances on available, computationally intensive Monte Carlo methods. We study here an advanced version of familiar Markov Chain Monte…
Model comparison and calibrated uncertainty quantification often require integrating over parameters, but scalable inference can be challenging for complex, multimodal targets. Nested Sampling is a robust alternative to standard MCMC, yet…
We propose a novel class of Sequential Monte Carlo (SMC) algorithms, appropriate for inference in probabilistic graphical models. This class of algorithms adopts a divide-and-conquer approach based upon an auxiliary tree-structured…
Computing geodesics for Riemannian manifolds is a difficult task that often relies on numerical approximations. However, these approximations tend to be either numerically unstable, have slow convergence, or scale poorly with manifold…
In Hamiltonian Monte Carlo sampling, the shape of the potential and the choice of the momentum distribution jointly give rise to the Hamiltonian dynamics of the sampler. An efficient sampler propagates quickly in all regions of the…