Related papers: Constrained Ensemble Langevin Monte Carlo
We introduce a novel framework for efficient sampling from complex, unnormalised target distributions by exploiting multiscale dynamics. Traditional score-based sampling methods either rely on learned approximations of the score function or…
We introduce a gradient-based learning method to automatically adapt Markov chain Monte Carlo (MCMC) proposal distributions to intractable targets. We define a maximum entropy regularised objective function, referred to as generalised speed…
Modern imaging methods rely strongly on Bayesian inference techniques to solve challenging imaging problems. Currently, the predominant Bayesian computation approach is convex optimisation, which scales very efficiently to high dimensional…
We study the efficiency of Thompson sampling for contextual bandits. Existing Thompson sampling-based algorithms need to construct a Laplace approximation (i.e., a Gaussian distribution) of the posterior distribution, which is inefficient…
Sampling from a high-dimensional distribution is a fundamental task in statistics, engineering, and the sciences. A canonical approach is the Langevin Algorithm, i.e., the Markov chain for the discretized Langevin Diffusion. This is the…
Bayesian inference for factorial hidden Markov models is challenging due to the exponentially sized latent variable space. Standard Monte Carlo samplers can have difficulties effectively exploring the posterior landscape and are often…
Sequential Monte Carlo (SMC) methods offer a principled approach to Bayesian uncertainty quantification but are traditionally limited by the need for full-batch gradient evaluations. We introduce a scalable variant by incorporating…
Hamiltonian Monte Carlo and underdamped Langevin Monte Carlo are state-of-the-art methods for taking samples from high-dimensional distributions with a differentiable density function. To generate samples, they numerically integrate…
Bayesian inference in complex generative models is often obstructed by the absence of tractable likelihoods and the infeasibility of computing gradients of high-dimensional simulators. Existing likelihood-free methods for generalized…
Sampling from various kinds of distributions is an issue of paramount importance in statistics since it is often the key ingredient for constructing estimators, test procedures or confidence intervals. In many situations, the exact sampling…
The celebrated Monte Carlo method estimates an expensive-to-compute quantity by random sampling. Bandit-based Monte Carlo optimization is a general technique for computing the minimum of many such expensive-to-compute quantities by adaptive…
In recent years, various interacting particle samplers have been developed to sample from complex target distributions, such as those found in Bayesian inverse problems. These samplers are motivated by the mean-field limit perspective and…
Random batch algorithms are constructed for quantum Monte Carlo simulations. The main objective is to alleviate the computational cost associated with the calculations of two-body interactions, including the pairwise interactions in the…
The problem of sampling constrained continuous distributions has frequently appeared in many machine/statistical learning models. Many Monte Carlo Markov Chain (MCMC) sampling methods have been adapted to handle different types of…
We analyse the performance of a recursive Monte Carlo method for the Bayesian estimation of the static parameters of a discrete--time state--space Markov model. The algorithm employs two layers of particle filters to approximate the…
In this paper we present a new approach to control variates for improving computational efficiency of Ensemble Monte Carlo. We present the approach using simulation of paths of a time-dependent nonlinear stochastic equation. The core idea…
We introduce a new Markov chain Monte Carlo (MCMC) sampler for infinite-dimensional inverse problems. Our new sampler is based on the affine invariant ensemble sampler, which uses interacting walkers to adapt to the covariance structure of…
Markov chain Monte Carlo is a class of algorithms for drawing Markovian samples from high-dimensional target densities to approximate the numerical integration associated with computing statistical expectation, especially in Bayesian…
Approximate Thompson sampling with Langevin Monte Carlo broadens its reach from Gaussian posterior sampling to encompass more general smooth posteriors. However, it still encounters scalability issues in high-dimensional problems when…
In the stochastic gradient descent (SGD) for sequential simulations such as the neural stochastic differential equations, the Multilevel Monte Carlo (MLMC) method is known to offer better theoretical computational complexity compared to the…