Related papers: Alternative sampling for variational quantum Monte…
In this article we study examples of systematic biases that can occur in quantum Monte Carlo methods due to the accumulation of non-linear expectation values, and approaches by which these errors can be corrected. We begin with a study of…
In many problems, complex non-Gaussian and/or nonlinear models are required to accurately describe a physical system of interest. In such cases, Monte Carlo algorithms are remarkably flexible and extremely powerful approaches to solve such…
Sequential Monte Carlo (SMC) algorithms were originally designed for estimating intractable conditional expectations within state-space models, but are now routinely used to generate approximate samples in the context of general-purpose…
We show that repulsive random variables can yield Monte Carlo methods with faster convergence rates than the typical $N^{-1/2}$, where $N$ is the number of integrand evaluations. More precisely, we propose stochastic numerical quadratures…
Driven by several successful applications such as in stochastic gradient descent or in Bayesian computation, control variates have become a major tool for Monte Carlo integration. However, standard methods do not allow the distribution of…
We study randomized quasi-Monte Carlo (RQMC) estimation of a multivariate integral where one of the variables takes only a finite number of values. This problem arises when the variable of integration is drawn from a mixture distribution as…
For important classes of many-fermion problems, quantum Monte Carlo (QMC) methods allow exact calculations of ground-state and finite-temperature properties, without the sign problem. The list spans condensed matter, nuclear physics, and…
Monte Carlo (MC) sampling algorithms are an extremely widely-used technique to estimate expectations of functions f(x), especially in high dimensions. Control variates are a very powerful technique to reduce the error of such estimates, but…
Monte Carlo approximations for random linear elliptic PDE constrained optimization problems are studied. We use empirical process theory to obtain best possible mean convergence rates $O(n^{-\frac{1}{2}})$ for optimal values and solutions,…
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…
We review the use of continuum quantum Monte Carlo (QMC) methods for the calculation of energy gaps from first principles, and present a broad set of excited-state calculations carried out with the variational and fixed-node diffusion QMC…
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…
In the day-to-day operation of a power system, the system operator repeatedly solves short-term generation planning problems. When formulating these problems the operators have to weigh the risk of costly failures against increased…
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…
Standard Monte Carlo computation is widely known to exhibit a canonical square-root convergence speed in terms of sample size. Two recent techniques, one based on control variate and one on importance sampling, both derived from an…
It is often necessary to make sampling-based statistical inference about many probability distributions in parallel. Given a finite computational resource, this article addresses how to optimally divide sampling effort between the samplers…
We consider the problem of estimating the expected outcomes of Monte Carlo processes whose outputs are described by multidimensional random variables. We tightly characterize the quantum query complexity of this problem for various choices…
Importance sampling is a popular variance reduction method for Monte Carlo estimation, where a notorious question is how to design good proposal distributions. While in most cases optimal (zero-variance) estimators are theoretically…
A resampling scheme provides a way to switch low-weight particles for sequential Monte Carlo with higher-weight particles representing the objective distribution. The less the variance of the weight distribution is, the more concentrated…