Related papers: An Introduction to Hamiltonian Monte Carlo Method …
We obtain several quantitative bounds on the mixing properties of the Hamiltonian Monte Carlo (HMC) algorithm for a strongly log-concave target distribution $\pi$ on $\mathbb{R}^{d}$, showing that HMC mixes quickly in this setting. One of…
Markov Chain Monte Carlo (MCMC) methods are a powerful tool for computation with complex probability distributions. However the performance of such methods is critically dependant on properly tuned parameters, most of which are difficult if…
In this work, we introduce a novel class of adaptive Monte Carlo methods, called adaptive independent sticky MCMC algorithms, for efficient sampling from a generic target probability density function (pdf). The new class of algorithms…
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…
Amongst Markov chain Monte Carlo algorithms, Hamiltonian Monte Carlo (HMC) is often the algorithm of choice for complex, high-dimensional target distributions; however, its efficiency is notoriously sensitive to the choice of the…
The hybrid Monte Carlo (HMC) algorithm is a ubiquitous method in computational physics with applications ranging from condensed matter to lattice QCD and beyond. However, HMC simulations often suffer from long autocorrelation times,…
We present a quantum Monte Carlo method capable of sampling the full density matrix of a many-particle system at finite temperature. This allows arbitrary reduced density matrix elements and expectation values of complicated non-local…
Hamiltonian Monte Carlo (HMC) is a widely deployed method to sample from high-dimensional distributions in Statistics and Machine learning. HMC is known to run very efficiently in practice and its popular second-order "leapfrog"…
The Bouncy Particle Sampler is a Markov chain Monte Carlo method based on a nonreversible piecewise deterministic Markov process. In this scheme, a particle explores the state space of interest by evolving according to a linear dynamics…
The performance of the Monte Carlo sampling methods relies on the crucial choice of a proposal density. The notion of optimality is fundamental to design suitable adaptive procedures of the proposal density within Monte Carlo schemes. This…
We present a method for performing Hamiltonian Monte Carlo that largely eliminates sample rejection for typical hyperparameters. In situations that would normally lead to rejection, instead a longer trajectory is computed until a new state…
Monte Carlo methods are essential tools for Bayesian inference. Gibbs sampling is a well-known Markov chain Monte Carlo (MCMC) algorithm, extensively used in signal processing, machine learning, and statistics, employed to draw samples from…
We propose a novel sequential Monte Carlo (SMC) method for sampling from unnormalized target distributions based on a reverse denoising diffusion process. While recent diffusion-based samplers simulate the reverse diffusion using…
Recent progress on the theory of variational hypocoercivity established that Randomized Hamiltonian Monte Carlo -- at criticality -- can achieve pronounced acceleration in its convergence and hence sampling performance over diffusive…
Stochastic Gradient Hamiltonian Monte Carlo (SGHMC) is a momentum version of stochastic gradient descent with properly injected Gaussian noise to find a global minimum. In this paper, non-asymptotic convergence analysis of SGHMC is given in…
Markov Chain Monte Carlo (MCMC) algorithms play an important role in statistical inference problems dealing with intractable probability distributions. Recently, many MCMC algorithms such as Hamiltonian Monte Carlo (HMC) and Riemannian…
The hybrid Monte Carlo (HMC) algorithm is applied for the Bayesian inference of the stochastic volatility (SV) model. We use the HMC algorithm for the Markov chain Monte Carlo updates of volatility variables of the SV model. First we…
In this paper, we consider a Bayesian inverse problem modeled by elliptic partial differential equations (PDEs). Specifically, we propose a data-driven and model-based approach to accelerate the Hamiltonian Monte Carlo (HMC) method in…
Bayesian inference is useful to obtain a predictive distribution with a small generalization error. However, since posterior distributions are rarely evaluated analytically, we employ the variational Bayesian inference or sampling method to…
Monte Carlo method is a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. They are often used in physical and mathematical problems and are most useful when it is difficult or…