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Orthogonal Monte Carlo (OMC) is a very effective sampling algorithm imposing structural geometric conditions (orthogonality) on samples for variance reduction. Due to its simplicity and superior performance as compared to its Quasi Monte…
Distributed learning methods have gained substantial momentum in recent years, with communication overhead often emerging as a critical bottleneck. Gradient compression techniques alleviate communication costs but involve an inherent…
Monte Carlo estimation in plays a crucial role in stochastic reaction networks. However, reducing the statistical uncertainty of the corresponding estimators requires sampling a large number of trajectories. We propose control variates…
We develop a Monte Carlo-free approach to inference post output from randomized algorithms with a convex loss and a convex penalty. The pivotal statistic based on a truncated law, called the selective pivot, usually lacks closed form…
We consider the problem of simulating loss probabilities and conditional excesses for linear asset portfolios under the t-copula model. Although in the literature on market risk management there are papers proposing efficient variance…
We present an adaptive multilevel Monte Carlo algorithm for solving the stochastic drift-diffusion-Poisson system with non-zero recombination rate. The a-posteriori error is estimated to enable goal-oriented adaptive mesh refinement for the…
The most common way to sample from a probability distribution is to use Monte-Carlo methods. For distributions on a continuous state space, one can find diffusions with the target distribution as equilibrium measure, so that the state of…
Probability measures supported on submanifolds can be sampled by adding an extra momentum variable to the state of the system, and discretizing the associated Hamiltonian dynamics with some stochastic perturbation in the extra variable. In…
We introduce new variants of classical regression-based algorithms for optimal stopping problems based on computation of regression coefficients by Monte Carlo approximation of the corresponding $L^2$ inner products instead of the…
In low-temperature high-density plasmas quantum effects of the electrons are becoming increasingly important. This requires the development of new theoretical and computational tools. Quantum Monte Carlo methods are among the most…
Engineering problems are often characterized by significant uncertainty in their material parameters. A typical example coming from geotechnical engineering is the slope stability problem where the soil's cohesion is modeled as a random…
Continuous-time quantum Monte Carlo refers to a class of algorithms designed to sample the thermal distribution of a quantum Hamiltonian through exact expansions of the Boltzmann exponential in terms of stochastic trajectories which are…
We present simple and practical strategies to reduce the variance of Monte Carlo estimators. Our focus is on variational Monte Carlo calculations of atomic forces and pressure in electronic systems, although we show that the underlying…
Reinforcement learning constantly deals with hard integrals, for example when computing expectations in policy evaluation and policy iteration. These integrals are rarely analytically solvable and typically estimated with the Monte Carlo…
An efficient Path Integral Monte Carlo procedure is proposed to simulate the behavior of quantum many-body dissipative systems described within the framework of the influence functional. Thermodynamic observables are obtained by Monte Carlo…
In this paper, we present a probabilistic numerical algorithm combining dynamic programming, Monte Carlo simulations and local basis regressions to solve non-stationary optimal multiple switching problems in infinite horizon. We provide the…
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…
Population Monte Carlo (PMC) sampling methods are powerful tools for approximating distributions of static unknowns given a set of observations. These methods are iterative in nature: at each step they generate samples from a proposal…
Control variates are a variance-reduction technique for Monte Carlo integration. The principle involves approximating the integrand by a function that can be analytically integrated, and integrating using the Monte Carlo method only the…
Employing nonparametric methods for density estimation has become routine in Bayesian statistical practice. Models based on discrete nonparametric priors such as Dirichlet Process Mixture (DPM) models are very attractive choices due to…