Related papers: A Conceptual Introduction to Hamiltonian Monte Car…
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…
Gaussian latent variable models are a key class of Bayesian hierarchical models with applications in many fields. Performing Bayesian inference on such models can be challenging as Markov chain Monte Carlo algorithms struggle with the…
The past few years have seen considerable progress in algorithmic development for the generation of gauge fields including the effects of dynamical fermions. The Rational Hybrid Monte Carlo (RHMC) algorithm, where Hybrid Monte Carlo is…
In most sampling algorithms, including Hamiltonian Monte Carlo, transition rates between states correspond to the probability of making a transition in a single time step, and are constrained to be less than or equal to 1. We derive a…
Population annealing Monte Carlo is an efficient sequential algorithm for simulating k-local Boolean Hamiltonians. Because of its structure, the algorithm is inherently parallel and therefore well suited for large-scale simulations of…
We study the integration of functions with respect to an unknown density. We compare the simple Monte Carlo method (which is almost optimal for a certain large class of inputs) and compare it with the Metropolis algorithm (based on a…
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…
Differentiable programming has emerged as a key programming paradigm empowering rapid developments of deep learning while its applications to important computational methods such as Monte Carlo remain largely unexplored. Here we present the…
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…
Markov chain Monte Carlo (MCMC) algorithms have long been the main workhorses of Bayesian inference. Among them, Hamiltonian Monte Carlo (HMC) has recently become very popular due to its efficiency resulting from effective use of the…
We present a scalable Bayesian framework for the analysis of confocal fluorescence spectroscopy data, addressing key limitations in traditional fluorescence correlation spectroscopy methods. Our framework captures molecular motion,…
Hamiltonian Flow Monte Carlo(HFMC) methods have been implemented in engineering, biology and chemistry. HFMC makes large gradient based steps to rapidly explore the state space. The application of the Hamiltonian dynamics allows to estimate…
In recent years dynamical systems (of deterministic and stochastic nature), describing many models in mathematics, physics, engineering and finances, become more and more complex. Numerical analysis narrowed only to deterministic algorithms…
Computing systems interacting with real-world processes must safely and reliably process uncertain data. The Monte Carlo method is a popular approach for computing with such uncertain values. This article introduces a framework for…
With our recently proposed effective Hamiltonian via Monte Carlo, we are able to compute low energy physics of quantum systems. The advantage is that we can obtain not only the spectrum of ground and excited states, but also wave functions.…
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…
Recently, the Hamilton Monte Carlo (HMC) has become widespread as one of the more reliable approaches to efficient sample generation processes. However, HMC is difficult to sample in a multimodal posterior distribution because the HMC chain…
This paper concerns the approximation of smooth, high-dimensional functions from limited samples using polynomials. This task lies at the heart of many applications in computational science and engineering - notably, some of those arising…
This technical report presents pseudo-code for a Riemannian manifold Hamiltonian Monte Carlo (RMHMC) method to efficiently simulate samples from $N$-dimensional posterior distributions $p(x|y)$, where $x \in R^N$ is drawn from a Gaussian…
We study cluster perturbation theory [Phys. Rev. Lett. \textbf{84}, 522 (2000)] when auxiliary field quantum Monte Carlo method is used for solving the cluster hamiltonian. As a case study, we calculate the spectral functions of the Hubbard…