Related papers: Symmetrically processed splitting integrators for …
We introduce a class of Monte Carlo estimators that aim to overcome the rapid growth of variance with dimension often observed for standard estimators by exploiting the target's independence structure. We identify the most basic…
Monte Carlo methods represent the "de facto" standard for approximating complicated integrals involving multidimensional target distributions. In order to generate random realizations from the target distribution, Monte Carlo techniques use…
We show how the integrators used for the molecular dynamics step of the Hybrid Monte Carlo algorithm can be further improved. These integrators not only approximately conserve some Hamiltonian $H$ but conserve exactly a nearby shadow…
We show how to improve the molecular dynamics step of Hybrid Monte Carlo, both by tuning the integrator using Poisson brackets measurements and by the use of force gradient integrators. We present results for moderate lattice sizes.
This paper derives two new optimization-driven Monte Carlo algorithms inspired from variable splitting and data augmentation. In particular, the formulation of one of the proposed approaches is closely related to the alternating direction…
The hierarchical Dirichlet process (HDP) has become an important Bayesian nonparametric model for grouped data, such as document collections. The HDP is used to construct a flexible mixed-membership model where the number of components is…
Symplectic integration algorithms have become popular in recent years in long-term orbital integrations because these algorithms enforce certain conservation laws that are intrinsic to Hamiltonian systems. For problems with large variations…
Riemannian manifold Hamiltonian Monte Carlo (RMHMC) is a powerful method of Bayesian inference that exploits underlying geometric information of the posterior distribution in order to efficiently traverse the parameter space. However, the…
Hamiltonian Monte Carlo (HMC) samples efficiently from high-dimensional posterior distributions with proposed parameter draws obtained by iterating on a discretized version of the Hamiltonian dynamics. The iterations make HMC…
Hamiltonian Monte Carlo is a popular sampling technique for smooth target densities. The scale lengths of the target have long been known to influence integration error and sampling efficiency. However, quantitative measures intrinsic to…
The efficient evaluation of high-dimensional integrals is of importance in both theoretical and practical fields of science, such as data science, statistical physics, and machine learning. However, exact computation methods suffer from the…
Hamiltonian Monte Carlo (HMC) is a powerful Markov chain Monte Carlo (MCMC) method for performing approximate inference in complex probabilistic models of continuous variables. In common with many MCMC methods, however, the standard HMC…
Monte Carlo integration is a powerful tool for scientific and statistical computation, but faces significant challenges when the integrand is a multi-modal distribution, even when the mode locations are known. This work introduces novel…
We unify slice sampling and Hamiltonian Monte Carlo (HMC) sampling, demonstrating their connection via the Hamiltonian-Jacobi equation from Hamiltonian mechanics. This insight enables extension of HMC and slice sampling to a broader family…
The hybrid Monte Carlo (HMC) algorithm is arguably the most efficient sampling method for general probability distributions of continuous variables. Together with exact Fourier acceleration (EFA) the HMC becomes equivalent to direct…
We explore two complementary modifications of the hybridization-expansion continuous-time Monte Carlo method, aiming at large multi-orbital quantum impurity problems. One idea is to compute the imaginary-time propagation using a matrix…
We suggest a numerical integration procedure for solving the equations of motion of certain classical spin systems which preserves the underlying symplectic structure of the phase space. Such symplectic integrators have been successfully…
We investigate the properties of the Hybrid Monte-Carlo algorithm (HMC) in high dimensions. HMC develops a Markov chain reversible w.r.t. a given target distribution $\Pi$ by using separable Hamiltonian dynamics with potential $-\log\Pi$.…
We study efficiency of higher order integrator schemes for the hybrid Monte Carlo (HMC) algorithm. Numerical tests are performed for Quantum Chromo Dynamics (QCD) with two flavors of Wilson fermions. We compare 2nd, 4th and 6th order…
Variational inference lies at the core of many state-of-the-art algorithms. To improve the approximation of the posterior beyond parametric families, it was proposed to include MCMC steps into the variational lower bound. In this work we…