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Monte Carlo sampling techniques have broad applications in machine learning, Bayesian posterior inference, and parameter estimation. Often the target distribution takes the form of a product distribution over a dataset with a large number…
We propose a hybrid generative model for efficient sampling of high-dimensional, multimodal probability distributions for Bayesian inference. Traditional Monte Carlo methods, such as the Metropolis-Hastings and Langevin Monte Carlo sampling…
Stochastic sampling methods are arguably the most direct and least intrusive means of incorporating parametric uncertainty into numerical simulations of partial differential equations with random inputs. However, to achieve an overall error…
We study the numerical integration of functions from isotropic Sobolev spaces $W_p^s([0,1]^d)$ using finitely many function evaluations within randomized algorithms, aiming for the smallest possible probabilistic error guarantee…
Estimating the density of a continuous random variable X has been studied extensively in statistics, in the setting where n independent observations of X are given a priori and one wishes to estimate the density from that. Popular methods…
Non-negative matrix factorization (NMF) is an important technique for obtaining low dimensional representations of datasets. However, classical NMF does not take into account data that is collected at different times or in different…
We present an algorithm to sample stochastic differential equations conditioned on rather general constraints, including integral constraints, endpoint constraints, and stochastic integral constraints. The algorithm is a pathspace…
Approximate Bayesian computation (ABC) methods are standard tools for inferring parameters of complex models when the likelihood function is analytically intractable. A popular approach to improving the poor acceptance rate of the basic…
Rendering algorithms typically integrate light paths over path space. However, integrating over this one unified space is not necessarily the most efficient approach, and we show that partitioning path space and integrating each of these…
A technique for reducing the number of integrals in a Monte Carlo calculation is introduced. For integrations relying on classical or mean-field trajectories with local weighting functions, it is possible to integrate analytically at least…
The main goal of this paper is to define and study new methods for the computation of effective coefficients in the homogenization of divergence-form operators with random coefficients. The methods introduced here are proved to have optimal…
A Monte Carlo method based on a density-of-states sampling is proposed for study of arbitrary statistical mechanical ensembles in a continuum. A random walk in the two-dimensional space of particle number and energy is used to estimate the…
We propose sequential Monte Carlo (SMC) methods for sampling the posterior distribution of state-space models under highly informative observation regimes, a situation in which standard SMC methods can perform poorly. A special case is…
We describe a novel simulation method that eliminates the slowing-down problem in the Monte Carlo simulations of imaginary-time path integrals near the continuum limit. This method combines a stochastic blocking procedure with the multigrid…
We describe a simple Importance Sampling strategy for Monte Carlo simulations based on a least squares optimization procedure. With several numerical examples, we show that such Least Squares Importance Sampling (LSIS) provides efficiency…
Improving efficiency of importance sampler is at the center of research in Monte Carlo methods. While adaptive approach is usually difficult within the Markov Chain Monte Carlo framework, the counterpart in importance sampling can be…
A non-parametric extension of control variates is presented. These leverage gradient information on the sampling density to achieve substantial variance reduction. It is not required that the sampling density be normalised. The novel…
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…
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…
Multiway data analysis aims to uncover patterns in data structured as multi-indexed arrays, with multiway covariance playing a crucial role in many applications. However, the high dimensionality of multiway covariance presents significant…