Related papers: Variance Reduction via Simultaneous Importance Sam…
Control variates are variance reduction tools for Monte Carlo estimators. They can provide significant variance reduction, but usually require a large number of samples, which can be prohibitive when sampling or evaluating the integrand is…
In this paper we present a new approach to control variates for improving computational efficiency of Ensemble Monte Carlo. We present the approach using simulation of paths of a time-dependent nonlinear stochastic equation. The core idea…
Variational Monte Carlo (VMC) is an approach for computing ground-state wavefunctions that has recently become more powerful due to the introduction of neural network-based wavefunction parametrizations. However, efficiently training neural…
In this article, we present a review of the recent developments on the topic of Multilevel Monte Carlo (MLMC) algorithm, in the paradigm of applications in financial engineering. We specifically focus on the recent studies conducted in two…
The sampling importance resampling method is widely utilized in various fields, such as numerical integration and statistical simulation. In this paper, two modified methods are presented by incorporating two variance reduction techniques…
In statistics and machine learning, approximation of an intractable integration is often achieved by using the unbiased Monte Carlo estimator, but the variances of the estimation are generally high in many applications. Control variates…
Monte Carlo methods are widely used importance sampling techniques for studying complex physical systems. Integrating these methods with deep learning has significantly improved efficiency and accuracy in high-dimensional problems and…
Classical algorithms in numerical analysis for numerical integration (quadrature/cubature) follow the principle of approximate and integrate: the integrand is approximated by a simple function (e.g. a polynomial), which is then integrated…
Control variates can be a powerful tool to reduce the variance of Monte Carlo estimators, but constructing effective control variates can be challenging when the number of samples is small. In this paper, we show that when a large number of…
The theme of the present paper is numerical integration of $C^r$ functions using randomized methods. We consider variance reduction methods that consist in two steps. First the initial interval is partitioned into subintervals and the…
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…
Monte Carlo methods are widely used for neutron transport simulations at least partly because of the accuracy they bring to the modeling of these problems. However, the computational burden associated with the slow convergence rate of Monte…
Importance sampling has been known as a powerful tool to reduce the variance of Monte Carlo estimator for rare event simulation. Based on the criterion of minimizing the variance of Monte Carlo estimator within a parametric family, we…
Monte Carlo integration with variance reduction by means of control variates can be implemented by the ordinary least squares estimator for the intercept in a multiple linear regression model with the integrand as response and the control…
We present a new adaptive Monte Carlo integration algorithm for ill-behaved integrands with non-factorizable singularities. The algorithm combines Vegas with multi channel sampling and performs significantly better than Vegas for a large…
The control variates method is a classical variance reduction technique for Monte Carlo estimators that exploits correlated auxiliary variables without introducing bias. In many applications, the quantity of interest can be expressed as a…
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 (MC) sampling is a popular method for estimating the statistics (e.g. expectation and variance) of a random variable. Its slow convergence has led to the emergence of advanced techniques to reduce the variance of the MC…
We describe a new algorithm, VEGAS+, for adaptive multidimensional Monte Carlo integration. The new algorithm adds a second adaptive strategy, adaptive stratified sampling, to the adaptive importance sampling that is the basis for its…
Variational Monte Carlo (VMC) is a powerful and fast-growing method for optimizing and evolving parameterized many-body wave functions, especially with modern neural-network quantum states. In practice, however, the stochastic estimators…