Related papers: A Multifidelity Monte Carlo Method for Realistic C…
We consider the problem of estimating expectations with respect to a target distribution with an unknown normalizing constant, and where even the unnormalized target needs to be approximated at finite resolution. This setting is ubiquitous…
This article reviews the application of advanced Monte Carlo techniques in the context of Multilevel Monte Carlo (MLMC). MLMC is a strategy employed to compute expectations which can be biased in some sense, for instance, by using the…
We present two Monte Carlo sampling algorithms for probabilistic inference that guarantee polynomial-time convergence for a larger class of network than current sampling algorithms provide. These new methods are variants of the known…
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…
We develop a multilevel Monte Carlo (MLMC) framework for uncertainty quantification with Monte Carlo dropout. Treating dropout masks as a source of epistemic randomness, we define a fidelity hierarchy by the number of stochastic forward…
The multi-level Monte Carlo method proposed by M. Giles (2008) approximates the expectation of some functionals applied to a stochastic process with optimal order of convergence for the mean-square error. In this paper, a modified…
This paper addresses optimization problems constrained by partial differential equations with uncertain coefficients. In particular, the robust control problem and the average control problem are considered for a tracking type cost…
Markov Chain Monte Carlo (MCMC) methods for sampling probability density functions (combined with abundant computational resources) have transformed the sciences, especially in performing probabilistic inferences, or fitting models to data.…
The problem of optimising functions with intractable gradients frequently arise in machine learning and statistics, ranging from maximum marginal likelihood estimation procedures to fine-tuning of generative models. Stochastic approximation…
Multilevel Monte Carlo can efficiently compute statistical estimates of discretized random variables, for a given error tolerance. Traditionally, only a certain statistic is computed from a particular implementation of multilevel Monte…
We propose a sequential Monte Carlo (SMC) method to efficiently and accurately compute cut-Bayesian posterior quantities of interest, variations of standard Bayesian approaches constructed primarily to account for model misspecification. We…
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…
Monte-Carlo simulations are routinely used for estimating the scaling exponents of complex systems. However, due to finite-size effects, determining the exponent values is often difficult and not reliable. Here we present a novel technique…
Because of their robustness, efficiency and non-intrusiveness, Monte Carlo methods are probably the most popular approach in uncertainty quantification to computing expected values of quantities of interest (QoIs). Multilevel Monte Carlo…
Multi-fidelity Monte Carlo methods leverage low-fidelity and surrogate models for variance reduction to make tractable uncertainty quantification even when numerically simulating the physical systems of interest with high-fidelity models is…
This study presents a comparative analysis of Monte Carlo (MC) and quasi-Monte Carlo (QMC) methods in the context of derivative pricing, emphasizing convergence rates and the curse of dimensionality. After a concise overview of traditional…
We construct Monte Carlo methods for the $L^2$-approximation in Hilbert spaces of multivariate functions sampling no more than $n$ function values of the target function. Their errors catch up with the rate of convergence and the…
We propose a generic Markov Chain Monte Carlo (MCMC) algorithm to speed up computations for datasets with many observations. A key feature of our approach is the use of the highly efficient difference estimator from the survey sampling…
Sequential Monte Carlo (SMC) methods are a class of techniques to sample approximately from any sequence of probability distributions using a combination of importance sampling and resampling steps. This paper is concerned with the…
Numerous applications in biology, statistics, science, and engineering require generating samples from high-dimensional probability distributions. In recent years, the Hamiltonian Monte Carlo (HMC) method has emerged as a state-of-the-art…