Related papers: Multi-level Monte Carlo acceleration of computatio…
We present and analyze a micro/macro acceleration technique for the Monte Carlo simulation of stochastic differential equations (SDEs) in which there is a separation between the (fast) time-scale on which individual trajectories of the SDE…
In this paper, we examine the Sample Average Approximation (SAA) procedure within a framework where the Monte Carlo estimator of the expectation is biased. We also introduce Multilevel Monte Carlo (MLMC) in the SAA setup to enhance the…
Machine Learning (ML) algorithms are increasingly used as surrogate models to increase the efficiency of stochastic reliability analyses in geotechnical engineering. This paper presents a highly efficient ML aided reliability technique that…
The generation of unit-weight events for complex scattering processes presents a severe challenge to modern Monte Carlo event generators. Even when using sophisticated phase-space sampling techniques adapted to the underlying transition…
Many problems in materials science and biology involve particles interacting with strong, short-ranged bonds, that can break and form on experimental timescales. Treating such bonds as constraints can significantly speed up sampling their…
We show how to speed up Sequential Monte Carlo (SMC) for Bayesian inference in large data problems by data subsampling. SMC sequentially updates a cloud of particles through a sequence of distributions, beginning with a distribution that is…
Hamiltonian Monte Carlo is a popular sampling technique for smooth target densities. The scale lengths of the target have long been known to influence integration error and sampling efficiency. However, quantitative measures intrinsic to…
In this paper, we propose and analyze a novel combination of multilevel Richardson-Romberg (ML2R) and importance sampling algorithm, with the aim of reducing the overall computational time, while achieving desired root-mean-squared error…
In this paper, we present a generalisation of the Multilevel Monte Carlo (MLMC) method to a setting where the level parameter is a continuous variable. This Continuous Level Monte Carlo (CLMC) estimator provides a natural framework in PDE…
Significance: Monte Carlo (MC) methods are the gold-standard for modeling light-tissue interactions due to their accuracy. Mesh-based MC (MMC) offers enhanced precision for complex tissue structures using tetrahedral mesh models. Despite…
Computing risk measures of a financial portfolio comprising thousands of derivatives is a challenging problem because (a) it involves a nested expectation requiring multiple evaluations of the loss of the financial portfolio for different…
We consider systems of stochastic differential equations with multiple scales and small noise and assume that the coefficients of the equations are ergodic and stationary random fields. Our goal is to construct provably-efficient importance…
We present a geometrically enhanced Markov chain Monte Carlo sampler for networks based on a discrete curvature measure defined on graphs. Specifically, we incorporate the concept of graph Forman curvature into sampling procedures on both…
Markov chain Monte Carlo methods are a powerful tool for sampling equilibrium configurations in complex systems. One problem these methods often face is slow convergence over large energy barriers. In this work, we propose a novel method…
Adaptive Monte Carlo methods are very efficient techniques designed to tune simulation estimators on-line. In this work, we present an alternative to stochastic approximation to tune the optimal change of measure in the context of…
Many machine learning problems involve Monte Carlo gradient estimators. As a prominent example, we focus on Monte Carlo variational inference (MCVI) in this paper. The performance of MCVI crucially depends on the variance of its stochastic…
An algorithm is proposed to solve robust control problems constrained by partial differential equations with uncertain coefficients, based on the so-called MG/OPT framework. The levels in this MG/OPT hierarchy correspond to discretization…
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…
We propose a novel sampling framework for inference in probabilistic models: an active learning approach that converges more quickly (in wall-clock time) than Markov chain Monte Carlo (MCMC) benchmarks. The central challenge in…
It is shown that superefficient Monte Carlo computations can be carried out by using chaotic dynamical systems as non-uniform random-number generators. Here superefficiency means that the expectation value of the square of the error…