Related papers: Combining Normalizing Flows and Quasi-Monte Carlo
Subject of this paper is the simplification of Markov chain Monte Carlo sampling as used in Bayesian statistical inference by means of normalising flows, a machine learning method which is able to construct an invertible and differentiable…
The recent introduction of machine learning techniques, especially normalizing flows, for the sampling of lattice gauge theories has shed some hope on improving the sampling efficiency of the traditional HMC algorithm. Naive use of…
We design and implement a novel algorithm for computing a multilevel Monte Carlo (MLMC) estimator of the cumulative distribution function of a quantity of interest in problems with random input parameters or initial conditions. Our approach…
Importance sampling is a rare event simulation technique used in Monte Carlo simulations to bias the sampling distribution towards the rare event of interest. By assigning appropriate weights to sampled points, importance sampling allows…
Monte Carlo (MC) sampling methods are widely applied in Bayesian inference, system simulation and optimization problems. The Markov Chain Monte Carlo (MCMC) algorithms are a well-known class of MC methods which generate a Markov chain with…
Markov chain Monte Carlo (MCMC) methods are widely used in machine learning. One of the major problems with MCMC is the question of how to design chains that mix fast over the whole state space; in particular, how to select the parameters…
Monte Carlo and Quasi-Monte Carlo methods present a convenient approach for approximating the expected value of a random variable. Algorithms exist to adaptively sample the random variable until a user defined absolute error tolerance is…
In general, the statistical simulation approaches are referred to as the Monte Carlo methods as a whole. The broad class of the Monte Carlo methods involves the Markov chain Monte Carlo (MCMC) techniques that attract the attention of…
Many machine learning problems optimize an objective that must be measured with noise. The primary method is a first order stochastic gradient descent using one or more Monte Carlo (MC) samples at each step. There are settings where…
Markov chain Monte Carlo (MCMC) is a sampling-based method for estimating features of probability distributions. MCMC methods produce a serially correlated, yet representative, sample from the desired distribution. As such it can be…
In many real-world engineering systems, the performance or reliability of the system is characterised by a scalar parameter. The distribution of this performance parameter is important in many uncertainty quantification problems, ranging…
Sequential Monte Carlo (SMC) is a methodology for sampling approximately from a sequence of probability distributions of increasing dimension and estimating their normalizing constants. We propose here an alternative methodology named…
We propose a renormalisation group inspired normalising flow that combines benefits from traditional Markov chain Monte Carlo methods and standard normalising flows to sample lattice field theories. Specifically, we use samples from a…
Population Monte Carlo (PMC) sampling methods are powerful tools for approximating distributions of static unknowns given a set of observations. These methods are iterative in nature: at each step they generate samples from a proposal…
The Markov chain Monte Carlo (MCMC) method is widely used in various fields as a powerful numerical integration technique for systems with many degrees of freedom. In MCMC methods, probabilistic state transitions can be considered as a…
We propose Continual Repeated Annealed Flow Transport Monte Carlo (CRAFT), a method that combines a sequential Monte Carlo (SMC) sampler (itself a generalization of Annealed Importance Sampling) with variational inference using normalizing…
This paper concerns the use of Markov chain Monte Carlo methods for posterior sampling in Bayesian nonparametric mixture models with normalized random measure priors. Making use of some recent posterior characterizations for the class of…
Hybrid Monte Carlo is a powerful Markov Chain Monte Carlo method for sampling from complex continuous distributions. However, a major limitation of HMC is its inability to be applied to discrete domains due to the lack of gradient signal.…
Monte Carlo simulations are widely used in many areas including particle accelerators. In this lecture, after a short introduction and reviewing of some statistical backgrounds, we will discuss methods such as direct inversion, rejection…
Importance Sampling (IS), an effective variance reduction strategy in Monte Carlo (MC) simulation, is frequently utilized for Bayesian inference and other statistical challenges. Quasi-Monte Carlo (QMC) replaces the random samples in MC…