Related papers: Variational and Monte Carlo Methods for Bayesian I…

We propose a projected semi-stochastic gradient descent method with mini-batch for improving both the theoretical complexity and practical performance of the general stochastic gradient descent method (SGD). We are able to prove linear…

We examine an analytic variational inference scheme for the Gaussian Process State Space Model (GPSSM) - a probabilistic model for system identification and time-series modelling. Our approach performs variational inference over both the…

In variational inference (VI), the practitioner approximates a high-dimensional distribution $\pi$ with a simple surrogate one, often a (product) Gaussian distribution. However, in many cases of practical interest, Gaussian distributions…

The stochastic volatility model is one of volatility models which infer latent volatility of asset returns. The Bayesian inference of the stochastic volatility (SV) model is performed by the hybrid Monte Carlo (HMC) algorithm which is…

Monte Carlo methods are widely used importance sampling techniques for studying complex physical systems. Integrating these methods with deep learning has significantly improved efficiency and accuracy in high-dimensional problems and…

The Dynamic Monte Carlo (DMC) method is an established molecular simulation technique for the analysis of the dynamics in colloidal suspensions. An excellent alternative to Brownian Dynamics or Molecular Dynamics simulation, DMC is…

Traditional regression models assume stationary relationships between predictors and responses, failing to capture the spatial heterogeneity present in many environmental, epidemiological, and ecological processes. To address this…

Stein variational gradient descent (SVGD) is a particle-based inference algorithm that leverages gradient information for efficient approximate inference. In this work, we enhance SVGD by leveraging preconditioning matrices, such as the…

Bayesian geoacoustic inversion problems are conventionally solved by Markov chain Monte Carlo methods or its variants, which are computationally expensive. This paper extends the classic Bayesian geoacoustic inversion framework by deriving…

Variational inference is a fast and scalable alternative to Markov chain Monte Carlo and has been widely applied to posterior inference tasks in statistics and machine learning. A traditional approach for implementing mean-field variational…

This paper provides a detailed theoretical analysis of methods to approximate the solutions of high-dimensional (>10^6) linear Bayesian problems. An optimal low-rank projection that maximizes the information content of the Bayesian…

Stein Variational Gradient Descent (SVGD) is a popular variational inference algorithm which simulates an interacting particle system to approximately sample from a target distribution, with impressive empirical performance across various…

We consider the numerical solution of scalar, nonlinear degenerate convection-diffusion problems with random diffusion coefficient and with random flux functions. Building on recent results on the existence, uniqueness and continuous…

Functional integral representations for solutions of the motion equations for wall-bounded incompressible viscous flows, expressed (implicitly) in terms of distributions of solutions to stochastic differential equations of McKean-Vlasov…

Stochastic gradient Markov Chain Monte Carlo (SGMCMC) is considered the gold standard for Bayesian inference in large-scale models, such as Bayesian neural networks. Since practitioners face speed versus accuracy tradeoffs in these models,…

This topical review describes the methodology of continuum variational and diffusion quantum Monte Carlo calculations. These stochastic methods are based on many-body wave functions and are capable of achieving very high accuracy. The…

Recently, Stochastic Gradient Markov Chain Monte Carlo (SG-MCMC) methods have been proposed for scaling up Monte Carlo computations to large data problems. Whilst these approaches have proven useful in many applications, vanilla SG-MCMC…

Stochastic variational inference offers an attractive option as a default method for differentiable probabilistic programming. However, the performance of the variational approach depends on the choice of an appropriate variational family.…

Generative diffusion models have recently emerged as a powerful strategy to perform stochastic sampling in Bayesian inverse problems, delivering remarkably accurate solutions for a wide range of challenging applications. However, diffusion…

Bayesian optimal experimental design (OED) seeks experiments that maximize the expected information gain (EIG) in model parameters. Directly estimating the EIG using nested Monte Carlo is computationally expensive and requires an explicit…