Related papers: Importance Gaussian Quadrature
Importance sampling (IS) is a technique that enables statistical estimation of output performance at multiple input distributions from a single nominal input distribution. IS is commonly used in Monte Carlo simulation for variance reduction…
Driven by several successful applications such as in stochastic gradient descent or in Bayesian computation, control variates have become a major tool for Monte Carlo integration. However, standard methods do not allow the distribution of…
Monte Carlo methods represent the "de facto" standard for approximating complicated integrals involving multidimensional target distributions. In order to generate random realizations from the target distribution, Monte Carlo techniques use…
The importance sampling (IS) method lies at the core of many Monte Carlo-based techniques. IS allows the approximation of a target probability distribution by drawing samples from a proposal (or importance) distribution, different from the…
Bayesian quadrature is a probabilistic, model-based approach to numerical integration, the estimation of intractable integrals, or expectations. Although Bayesian quadrature was popularised already in the 1980s, no systematic and…
The study further explores randomized QMC (RQMC), which maintains the QMC convergence rate and facilitates computational efficiency analysis. Emphasis is laid on integrating randomly shifted lattice rules, a distinct RQMC quadrature, with…
This article is concerned with Gaussian process quadratures, which are numerical integration methods based on Gaussian process regression methods, and sigma-point methods, which are used in advanced non-linear Kalman filtering and smoothing…
Importance sampling (IS) as an elegant and efficient variance reduction (VR) technique for the acceleration of stochastic optimization problems has attracted many researches recently. Unlike commonly adopted stochastic uniform sampling in…
Multiple importance sampling (MIS) is an increasingly used methodology where several proposal densities are used to approximate integrals, generally involving target probability density functions. The use of several proposals allows for a…
Multiple Importance Sampling (MIS) methods approximate moments of complicated distributions by drawing samples from a set of proposal distributions. Several ways to compute the importance weights assigned to each sample have been recently…
The Integrated Nested Laplace Approximation (INLA) is a deterministic approach to Bayesian inference on latent Gaussian models (LGMs) and focuses on fast and accurate approximation of posterior marginals for the parameters in the models.…
Bayesian probabilistic numerical methods are a set of tools providing posterior distributions on the output of numerical methods. The use of these methods is usually motivated by the fact that they can represent our uncertainty due to…
The basic idea of importance sampling is to use independent samples from a proposal measure in order to approximate expectations with respect to a target measure. It is key to understand how many samples are required in order to guarantee…
Importance sampling is a Monte Carlo method that introduces a proposal distribution to sample the space according to the target distribution. Yet calibration of the proposal distribution is essential to achieving efficiency, thus the resort…
Approximate inference in probability models is a fundamental task in machine learning. Approximate inference provides powerful tools to Bayesian reasoning, decision making, and Bayesian deep learning. The main goal is to estimate the…
Probabilistic graphical models are powerful tools which allow us to formalise our knowledge about the world and reason about its inherent uncertainty. There exist a considerable number of methods for performing inference in probabilistic…
We consider importance sampling (IS) type weighted estimators based on Markov chain Monte Carlo (MCMC) targeting an approximate marginal of the target distribution. In the context of Bayesian latent variable models, the MCMC typically…
Gaussian Quadrature is a well known technique for numerical integration. Recently Gaussian quadrature with respect to discrete measures corresponding to finite sums have found some new interest. In this paper we apply these ideas to…
The self-normalized importance sampling (SNIS) estimator is a Monte Carlo estimator widely used to approximate expectations in statistical signal processing and machine learning. The efficiency of SNIS depends on the choice of proposal, but…
We consider the sample efficient estimation of failure probabilities from expensive oracle evaluations of a limit state function via importance sampling (IS). In contrast to conventional ``two stage'' approaches, which first train a…