Related papers: Sampling with Riemannian Hamiltonian Monte Carlo i…
We give the first rigorous proof of the convergence of Riemannian Hamiltonian Monte Carlo, a general (and practical) method for sampling Gibbs distributions. Our analysis shows that the rate of convergence is bounded in terms of natural…
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…
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…
Hamiltonian Monte Carlo (HMC) has been widely adopted in the statistics community because of its ability to sample high-dimensional distributions much more efficiently than other Metropolis-based methods. Despite this, HMC often performs…
Hierarchical Bayesian models based on Gaussian processes are considered useful for describing complex nonlinear statistical dependencies among variables in real-world data. However, effective Monte Carlo algorithms for inference with these…
Restricted Boltzmann Machines are simple and powerful generative models that can encode any complex dataset. Despite all their advantages, in practice the trainings are often unstable and it is difficult to assess their quality because the…
Riemann manifold Hamiltonian Monte Carlo (RMHMC) has the potential to produce high-quality Markov chain Monte Carlo-output even for very challenging target distributions. To this end, a symmetric positive definite scaling matrix for RMHMC,…
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…
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…
Assuming a steady-state condition within a cell, metabolic fluxes satisfy an under-determined linear system of stoichiometric equations. Characterizing the space of fluxes that satisfy such equations along with given bounds (and possibly…
Leveraging the coherent exploration of Hamiltonian flow, Hamiltonian Monte Carlo produces computationally efficient Monte Carlo estimators, even with respect to complex and high-dimensional target distributions. When confronted with…
Even in low dimensions, sampling from multi-modal distributions is challenging. We provide the first sampling algorithm for a broad class of distributions -- including all Gaussian mixtures -- with a query complexity that is polynomial in…
Hamiltonian Monte Carlo (HMC) is a Markov chain algorithm for sampling from a high-dimensional distribution with density $e^{-f(x)}$, given access to the gradient of $f$. A particular case of interest is that of a $d$-dimensional Gaussian…
In this article, we describe a {\tt R} package for sampling from an empirical likelihood-based posterior using a Hamiltonian Monte Carlo method. Empirical likelihood-based methodologies have been used in Bayesian modeling of many problems…
Sampling from hierarchical Bayesian models is often difficult for MCMC methods, because of the strong correlations between the model parameters and the hyperparameters. Recent Riemannian manifold Hamiltonian Monte Carlo (RMHMC) methods have…
We give lower bounds on the performance of two of the most popular sampling methods in practice, the Metropolis-adjusted Langevin algorithm (MALA) and multi-step Hamiltonian Monte Carlo (HMC) with a leapfrog integrator, when applied to…
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…
In this work we present a new and efficient Bayesian method for nonlinear three dimensional large scale structure inference. We employ a Hamiltonian Monte Carlo (HMC) sampler to obtain samples from a multivariate highly non-Gaussian…
Recent studies into the properties of quantum statistical ensembles in high-dimensional Hilbert spaces have encountered difficulties associated with the Monte-Carlo sampling of quantum superpositions constrained by the energy expectation…
We study randomized algorithms for constrained optimization, in abstract frameworks that include, in strictly increasing generality: convex programming; LP-type problems; violator spaces; and a setting we introduce, consistent spaces. Such…