Related papers: Preconditioning Hamiltonian Monte Carlo by minimiz…

Bayesian inference has many advantages for complex models, but standard Monte Carlo methods for summarizing the posterior can be computationally demanding, and it is attractive to consider optimization-based variational methods. Our work…

In this paper, we propose Barrier Hamiltonian Monte Carlo (BHMC), a version of the HMC algorithm which aims at sampling from a Gibbs distribution $\pi$ on a manifold $\mathrm{M}$, endowed with a Hessian metric $\mathfrak{g}$ derived from a…

The Diffusion Monte Carlo (DMC) method is applied to the water monomer, dimer, and hexamer, using q-TIP4P/F, one of the most simple, empirical water models with flexible monomers. The bias in the time step ($\Delta\tau$) and population size…

We present dimension-free convergence and discretization error bounds for the unadjusted Hamiltonian Monte Carlo algorithm applied to high-dimensional probability distributions of mean-field type. These bounds require the discretization…

Hamiltonian Monte Carlo (HMC) has emerged as a powerful Markov Chain Monte Carlo (MCMC) method to sample from complex continuous distributions. However, a fundamental limitation of HMC is that it can not be applied to distributions with…

We present Monte Carlo estimates for site and bond percolation thresholds in simple hypercubic lattices with 4 to 13 dimensions. For d<6 they are preliminary, for d >= 6 they are between 20 to 10^4 times more precise than the best previous…

Numerous applications in biology, statistics, science, and engineering require generating samples from high-dimensional probability distributions. In recent years, the Hamiltonian Monte Carlo (HMC) method has emerged as a state-of-the-art…

Hybrid Monte Carlo (HMC) generates samples from a prescribed probability distribution in a configuration space by simulating Hamiltonian dynamics, followed by the Metropolis (-Hastings) acceptance/rejection step. Compressible HMC (CHMC)…

Bayesian max-margin models have shown superiority in various practical applications, such as text categorization, collaborative prediction, social network link prediction and crowdsourcing, and they conjoin the flexibility of Bayesian…

For big data analysis, high computational cost for Bayesian methods often limits their applications in practice. In recent years, there have been many attempts to improve computational efficiency of Bayesian inference. Here we propose an…

The Fisher information matrix provides a way to measure the amount of information given observed data based on parameters of interest. Many applications of the FIM exist in statistical modeling, system identification, and parameter…

We introduce an approach based on mirror descent and sequential Monte Carlo (SMC) to perform joint parameter inference and posterior estimation in latent variable models. This approach is based on minimisation of a functional over the…

The median absolute deviation is a widely used robust measure of statistical dispersion. Using a scale constant, we can use it as an asymptotically consistent estimator for the standard deviation under normality. For finite samples, the…

We propose a new framework of variance-reduced Hamiltonian Monte Carlo (HMC) methods for sampling from an $L$-smooth and $m$-strongly log-concave distribution, based on a unified formulation of biased and unbiased variance reduction…

Hutchinson's method estimates the trace of a matrix function $f(D)$ stochastically using samples $\tau^Hf(D)\tau$, where the components of the random vectors $\tau$ obey an isotropic probability distribution. Estimating the trace of the…

The Hamiltonian Monte Carlo (HMC) algorithm is a powerful Markov Chain Monte Carlo (MCMC) method that uses Hamiltonian dynamics to generate samples from a target distribution. To fully exploit its potential, we must understand how…

We propose an adaptive MCMC method that learns a linear preconditioner which is dense in its off-diagonal elements but sparse in its parametrisation. Due to this sparsity, we achieve a per-iteration computational complexity of $O(m^2d)$ for…

We propose Pathfinder, a variational method for approximately sampling from differentiable log densities. Starting from a random initialization, Pathfinder locates normal approximations to the target density along a quasi-Newton…

Hamiltonian Monte Carlo (HMC) is a powerful and accurate method to sample from the posterior distribution in Bayesian inference. However, HMC techniques are computationally demanding for Bayesian neural networks due to the high…

Bayesian inference in the presence of an intractable likelihood function is computationally challenging. When following a Markov chain Monte Carlo (MCMC) approach to approximate the posterior distribution in this context, one typically…