Related papers: Note on the geodesic Monte Carlo
We investigate the effect of using local and non-local second derivative information on the performance of Hamiltonian Monte Carlo (HMC) sampling methods, for high-dimension non-Gaussian distributions, with application to Bayesian inference…
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…
Deep Gaussian Processes (DGPs) are hierarchical generalizations of Gaussian Processes that combine well calibrated uncertainty estimates with the high flexibility of multilayer models. One of the biggest challenges with these models is that…
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…
Approximate inference in probabilistic graphical models (PGMs) can be grouped into deterministic methods and Monte-Carlo-based methods. The former can often provide accurate and rapid inferences, but are typically associated with biases…
Hamiltonian Monte Carlo (HMC) and its dynamic extensions, such as the No-U-Turn Sampler (NUTS), are powerful Markov chain Monte Carlo methods for sampling from complex, high-dimensional probability distributions. Riemannian manifold…
The use of the probabilistic approach to solve inverse problems is becoming more popular in the geophysical community, thanks to its ability to address nonlinear forward problems and to provide uncertainty quantification. However, such…
The Hamiltonian Monte Carlo method generates samples by introducing a mechanical system that explores the target density. For distributions on manifolds it is not always simple to perform the mechanics as a result of the lack of global…
The advantages of sequential Monte Carlo (SMC) are exploited to develop parameter estimation and model selection methods for GARCH (Generalized AutoRegressive Conditional Heteroskedasticity) style models. It provides an alternative method…
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…
This paper introduces a Bayesian framework that combines Markov chain Monte Carlo (MCMC) sampling, dimensionality reduction, and neural density estimation to efficiently handle inverse problems that (i) must be solved multiple times, and…
Markov Chain Monte Carlo (MCMC) is a computational approach to fundamental problems such as inference, integration, optimization, and simulation. The field has developed a broad spectrum of algorithms, varying in the way they are motivated,…
We present an efficient algorithm for the inference of stochastic block models in large networks. The algorithm can be used as an optimized Markov chain Monte Carlo (MCMC) method, with a fast mixing time and a much reduced susceptibility to…
Orthogonal Monte Carlo (OMC) is a very effective sampling algorithm imposing structural geometric conditions (orthogonality) on samples for variance reduction. Due to its simplicity and superior performance as compared to its Quasi Monte…
Matrix normal models have an associated 4-tensor for their covariance representation. The covariance array associated with a matrix normal model is naturally represented as a Kronecker-product structured covariance associated with the…
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…
We generalize the Hamiltonian Monte Carlo algorithm with a stack of neural network layers and evaluate its ability to sample from different topologies in a two dimensional lattice gauge theory. We demonstrate that our model is able to…
Markov chain Monte Carlo (MCMC) methods are fundamental to Bayesian computation, but can be computationally intensive, especially in high-dimensional settings. Push-forward generative models, such as generative adversarial networks (GANs),…
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…
In Bayesian inference, Hamiltonian Monte Carlo (HMC) is a popular Markov Chain Monte Carlo (MCMC) algorithm known for its efficiency in sampling from complex probability distributions. However, its application to models with latent…