Related papers: Monte Carlo with Determinantal Point Processes
This paper develops and analyzes an efficient numerical method for solving elliptic partial differential equations, where the diffusion coefficients are random perturbations of deterministic diffusion coefficients. The method is based upon…
Monte Carlo experiments produce samples in order to estimate features of a given distribution. However, simultaneous estimation of means and quantiles has received little attention, despite being common practice. In this setting we…
Recursive Monte Carlo filters, also called particle filters, are a powerful tool to perform computations in general state space models. We discuss and compare the accept--reject version with the more common sampling importance resampling…
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…
While multilevel Monte Carlo (MLMC) methods for the numerical approximation of partial differential equations with random coefficients enjoy great popularity, combinations with spatial adaptivity seem to be rare. We present an adaptive MLMC…
Motivated mainly by applications to partial differential equations with random coefficients, we introduce a new class of Monte Carlo estimators, called Toeplitz Monte Carlo (TMC) estimator for approximating the integral of a multivariate…
In Quasi-Monte Carlo integration, the integration error is believed to be generally smaller than in classical Monte Carlo with the same number of integration points. Using an appropriate definition of an ensemble of quasi-randompoint sets,…
For basic machine learning problems, expected error is used to evaluate model performance. Since the distribution of data is usually unknown, we can make simple hypothesis that the data are sampled independently and identically distributed…
We develop a Monte-Carlo based numerical method for solving discrete-time stochastic optimal control problems with inventory. These are optimal control problems in which the control affects only a deterministically evolving inventory…
A Monte Carlo method for computing the action of a matrix exponential for a certain class of matrices on a vector is proposed. The method is based on generating random paths, which evolve through the indices of the matrix, governed by a…
We introduce and analyze a parallel sequential Monte Carlo methodology for the numerical solution of optimization problems that involve the minimization of a cost function that consists of the sum of many individual components. The proposed…
The Multilevel Monte Carlo method is an efficient variance reduction technique. It uses a sequence of coarse approximations to reduce the computational cost in uncertainty quantification applications. The method is nowadays often considered…
In this study, we give an extension of Montanaro's arXiv/archive:1504.06987 quantum Monte Carlo method, tailored for computing expected values of random variables that exhibit infinite variance. This addresses a challenge in analyzing…
Monte Carlo methods play important part in modern statistical physics. The application of these methods suffer from two main difficulties.The first is caused by the relatively small number of particles that can participate in any numerical…
This paper studies the rate of convergence for conditional quasi-Monte Carlo (QMC), which is a counterpart of conditional Monte Carlo. We focus on discontinuous integrands defined on the whole of $R^d$, which can be unbounded. Under…
While the Quasi-Monte Carlo method of numerical integration achieves smaller integration error than standard Monte Carlo, its use in particle physics phenomenology has been hindered by the abscence of a reliable way to estimate that error.…
In this work, we propose a smart idea to couple importance sampling and Multilevel Monte Carlo (MLMC). We advocate a per level approach with as many importance sampling parameters as the number of levels, which enables us to compute the…
We propose and analyze a method for computing failure probabilities of systems modeled as numerical deterministic models (e.g., PDEs) with uncertain input data. A failure occurs when a functional of the solution to the model is below (or…
We study random compressible viscous magnetohydrodynamic flows. Combining the Monte Carlo method with a deterministic finite volume method we solve the random system numerically. Quantitative error estimates including statistical and…
Bootstrapping was designed to randomly resample data from a fixed sample using Monte Carlo techniques. However, the original sample itself defines a discrete distribution. Convolutional methods are well suited for discrete distributions,…