Related papers: Introduction to stochastic error correction method…
Nested sampling is a simulation method for approximating marginal likelihoods proposed by Skilling (2006). We establish that nested sampling has an approximation error that vanishes at the standard Monte Carlo rate and that this error is…
Sampling occupies an important position in theories of various scientific fields, and Markov chain Monte Carlo (MCMC) provides the most common technique of sampling. In the progress of MCMC, a huge number of studies have aimed the…
In this paper we propose a novel numerical approach for the Boltzmann equation with uncertainties. The method combines the efficiency of classical direct simulation Monte Carlo (DSMC) schemes in the phase space together with the accuracy of…
In this paper, we propose and analyze a new stochastic homogenization method for diffusion equations with random and fast oscillatory coefficients. In the proposed method, the homogenized solutions are sought through a two-stage procedure.…
We provide a pedagogical introduction to the two main variants of real-space quantum Monte Carlo methods for electronic-structure calculations: variational Monte Carlo (VMC) and diffusion Monte Carlo (DMC). Assuming no prior knowledge on…
The simulation of the expectation of a stochastic quantity E[Y] by Monte Carlo methods is known to be computationally expensive especially if the stochastic quantity or its approximation Y_n is expensive to simulate, e.g., the solution of a…
Over the last few years there have been dramatic advances in our understanding of mathematical and computational models of complex systems in the presence of uncertainty. This has led to a growth in the area of uncertainty quantification as…
Uncertainties have become a major concern in integrated circuit design. In order to avoid the huge number of repeated simulations in conventional Monte Carlo flows, this paper presents an intrusive spectral simulator for statistical circuit…
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…
In recent years, randomized methods for numerical linear algebra have received growing interest as a general approach to large-scale problems. Typically, the essential ingredient of these methods is some form of randomized dimension…
We introduce a new class of Monte Carlo based approximations of expectations of random variables such that their laws are only available via certain discretizations. Sampling from the discretized versions of these laws can typically…
We investigate the properties of a sequential Monte Carlo method where the particle weight that appears in the algorithm is estimated by a positive, unbiased estimator. We present broadly-applicable convergence results, including a central…
Stochastic Galerkin methods offer unexplored potential for the numerical simulation of parabolic problems with random variables, in particular if they are combined with variational discretizations of the space and time variables. Due to the…
Quantiles and expected shortfalls are usually used to measure risks of stochastic systems, which are often estimated by Monte Carlo methods. This paper focuses on the use of quasi-Monte Carlo (QMC) method, whose convergence rate is…
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…
We present a novel variant of the multi-level Monte Carlo method that effectively utilizes a reserved computational budget on a high-performance computing system to minimize the mean squared error. Our approach combines concepts of the…
Sufficient dimension reduction is a powerful tool to extract core information hidden in the high-dimensional data and has potentially many important applications in machine learning tasks. However, the existing nonlinear sufficient…
We introduce a new diagonalization method called quasi-sparse eigenvector diagonalization which finds the most important basis vectors of the low energy eigenstates of a quantum Hamiltonian. It can operate using any basis, either orthogonal…
The "backward simulation" of a stochastic process is defined as the stochastic dynamics that trace a time-reversed path from the target region to the initial configuration. If the probabilities calculated by the original simulation are…
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…