Related papers: Using Monte Carlo to optimize variable cuts
Much recent research has been conducted in the area of Bayesian learning, particularly with regard to the optimization of hyper-parameters via Gaussian process regression. The methodologies rely chiefly on the method of maximizing the…
Monte Carlo simulations are widely used in many areas including particle accelerators. In this lecture, after a short introduction and reviewing of some statistical backgrounds, we will discuss methods such as direct inversion, rejection…
Statistical signal processing applications usually require the estimation of some parameters of interest given a set of observed data. These estimates are typically obtained either by solving a multi-variate optimization problem, as in the…
Variational quantum algorithms are poised to have significant impact on high-dimensional optimization, with applications in classical combinatorics, quantum chemistry, and condensed matter. Nevertheless, the optimization landscape of these…
Wave-function Monte Carlo methods are an important tool for simulating quantum systems, but the standard method cannot be used to simulate decoherence in continuously measured systems. Here we present a new Monte Carlo method for such…
Kinetic equations play a major rule in modeling large systems of interacting particles. Uncertainties may be due to various reasons, like lack of knowledge on the microscopic interaction details or incomplete informations at the boundaries.…
We introduce a stochastic version of the cutting-plane method for a large class of data-driven Mixed-Integer Nonlinear Optimization (MINLO) problems. We show that under very weak assumptions the stochastic algorithm is able to converge to…
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…
One of the leading candidates for near-term quantum advantage is the class of Variational Quantum Algorithms, but these algorithms suffer from classical difficulty in optimizing the variational parameters as the number of parameters…
In the nano era in integrated circuit fabrication technologies, the performance variability due to statistical process and circuit parameter variations is becoming more and more significant. Considerable effort has been expended in the EDA…
This work introduces a novel multilevel Monte Carlo (MLMC) metamodeling approach for variance function estimation. Although devising an efficient experimental design for simulation metamodeling can be elusive, the MLMC-based approach…
We review the method of stochastic error correction which eliminates the truncation error associated with any subspace diagonalization. Monte Carlo sampling is used to compute the contribution of the remaining basis vectors not included in…
We present an exact Monte Carlo algorithm designed to sample theories where the energy is a sum of many couplings of decreasing strength. The algorithm avoids the computation of almost all non-leading terms. Its use is illustrated by…
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 present general principles for the design and analysis of unbiased Monte Carlo estimators in a wide range of settings. Our estimators posses finite work-normalized variance under mild regularity conditions. We apply our estimators to…
We use a variational Monte Carlo algorithm to solve the electronic structure of two-dimensional semiconductor quantum dots in external magnetic field. We present accurate many-body wave functions for the system in various magnetic field…
Conditional Monte Carlo or pre-integration is a powerful tool for reducing variance and improving the regularity of integrands when using Monte Carlo and quasi-Monte Carlo (QMC) methods. To select the variable to pre-integrate, one must…
Consider a central problem in randomized approximation schemes that use a Monte Carlo approach. Given a sequence of independent, identically distributed random variables $X_1,X_2,\ldots$ with mean $\mu$ and standard deviation at most $c…
The kinetic Monte Carlo method is a standard approach for simulating physical systems whose dynamics are stochastic or that evolve in a probabilistic manner. Here we show how to calculate the system time for such simulations.
Measuring observables to constrain models using maximum-likelihood estimation is fundamental to many physics experiments. Wilks' theorem provides a simple way to construct confidence intervals on model parameters, but it only applies under…