Related papers: Zero-variance principle for Monte Carlo algorithms
Quantum computing is a promising way to systematically solve the longstanding computational problem, the ground state of a many-body fermion system. Many efforts have been made to realise certain forms of quantum advantage in this problem,…
The main focus of this article is to provide a mathematical study of the algorithm proposed in \cite{boyaval2010variance} where the authors proposed a variance reduction technique for the computation of parameter-dependent expectations…
Quantum computing was so far mainly concerned with discrete problems. Recently, E. Novak and the author studied quantum algorithms for high dimensional integration and dealt with the question, which advantages quantum computing can bring…
We derive the improved estimators for general interactions and employ these for the continuous-time quantum Monte Carlo method. Using a worm algorithm we show how measuring higher-ordered correlators leads to an improved high-frequency…
We describe a Monte Carlo procedure which allows sampling of the disjoint configuration spaces associated with crystalline and fluid phases, within a single simulation. The method utilises biased sampling techniques to enhance the…
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…
Adaptive importance sampling is a widely spread Monte Carlo technique that uses a re-weighting strategy to iteratively estimate the so-called target distribution. A major drawback of adaptive importance sampling is the large variance of the…
In this paper, we aim to compute numerical approximation integral by using an adaptive Monte Carlo algorithm. We propose a stratified sampling algorithm based on an iterative method which splits the strata following some quantities called…
We propose a variance reduction framework for variational inference using the Multilevel Monte Carlo (MLMC) method. Our framework is built on reparameterized gradient estimators and "recycles" parameters obtained from past update history in…
Population Monte Carlo has been introduced as a sequential importance sampling technique to overcome poor fit of the importance function. In this paper, we compare the performances of the original Population Monte Carlo algorithm with a…
The Monte Carlo algorithm is increasingly utilized, with its central step involving computer-based random sampling from stochastic models. While both Markov Chain Monte Carlo (MCMC) and Reject Monte Carlo serve as sampling methods, the…
In ordinary importance sampling with a nonnegative integrand there exists an importance sampling strategy with zero variance. Practical sampling strategies are often based on approximating that optimal solution, potentially approaching zero…
Variational wave functions used in the variational Monte Carlo (VMC) method are extensively improved to overcome the biases coming from the assumed variational form of the wave functions. We construct a highly generalized variational form…
We present a Monte Carlo algorithm that allows the simultaneous determination of a few extremal eigenpairs of a very large matrix without the need to compute the inner product of two vectors or store all the components of any one vector.…
Monte Carlo method is a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. They are often used in physical and mathematical problems and are most useful when it is difficult or…
Zero-variance control variates (ZV-CV) are a post-processing method to reduce the variance of Monte Carlo estimators of expectations using the derivatives of the log target. Once the derivatives are available, the only additional…
In this paper we present a novel approach towards variance reduction for discretised diffusion processes. The proposed approach involves specially constructed control variates and allows for a significant reduction in the variance for the…
Constructing more expressive ansatz has been a primary focus for quantum Monte Carlo, aimed at more accurate \textit{ab initio} calculations. However, with more powerful ansatz, e.g. various recent developed models based on neural-network…
We investigate Monte Carlo energy and variance minimization techniques for optimizing many-body wave functions. Several variants of the basic techniques are studied, including limiting the variations in the weighting factors which arise in…
Monte Carlo integration is a commonly used technique to compute intractable integrals and is typically thought to perform poorly for very high-dimensional integrals. To show that this is not always the case, we examine Monte Carlo…