Related papers: Comparative Analysis of Numerical Methods for Para…
We consider a high dimensional binary classification problem and construct a classification procedure by minimizing the empirical misclassification risk with a penalty on the number of selected features. We derive non-asymptotic probability…
The Monte Carlo method is a thriving and mathematically beautiful numerical technique used extensively, nowadays, to deal with many demanding problems in diverse fields. Here, we present an iterative Monte Carlo algorithm to work out very…
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…
In recent years dynamical systems (of deterministic and stochastic nature), describing many models in mathematics, physics, engineering and finances, become more and more complex. Numerical analysis narrowed only to deterministic algorithms…
We introduce Preconditioned Monte Carlo (PMC), a novel Monte Carlo method for Bayesian inference that facilitates efficient sampling of probability distributions with non-trivial geometry. PMC utilises a Normalising Flow (NF) in order to…
A quantum Monte Carlo method combining update of the loop algorithm with the global flip of the world line is proposed as an efficient method to study the magnetization process in an external field, which has been difficult because of…
In this work we propose a hierarchy of Monte Carlo methods for sampling equilibrium properties of stochastic lattice systems with competing short and long range interactions. Each Monte Carlo step is composed by two or more sub - steps…
The order of convergence of the Monte Carlo method is 1/2 which means that we need quadruple samples to decrease the error in half in the numerical simulation. Multilevel Monte Carlo methods reach the same order of error by spending less…
In a multi-fidelity setting, data are available from two sources, high- and low-fidelity. Low-fidelity data has larger size and can be leveraged to make more efficient inference about quantities of interest, e.g. the mean, for high-fidelity…
We present a comparison between a number of recently introduced low-memory wave function optimization methods for variational Monte Carlo in which we find that first and second derivative methods possess strongly complementary relative…
Douglas-Rachford splitting and its equivalent dual formulation ADMM are widely used iterative methods in composite optimization problems arising in control and machine learning applications. The performance of these algorithms depends on…
Although the linear method is one of the most robust algorithms for optimizing non-linearly parametrized wavefunctions in variational Monte Carlo, it suffers from a memory bottleneck due to the fact at each optimization step a generalized…
Competing phases or interactions in complex many-particle systems can result in free energy barriers that strongly suppress thermal equilibration. Here we discuss how extended ensemble Monte Carlo simulations can be used to study the…
In many applications, it is of interest to approximate data, given by mxn matrix A, by a matrix B of at most rank k, which is much smaller than m and n. The best approximation is given by singular value decomposition, which is too time…
I discuss optimized data analysis and Monte Carlo methods. Reweighting methods are discussed through examples, like Lee-Yang zeroes in the Ising model and the absence of deconfinement in QCD. I discuss reweighted data analysis and…
A novel method for extracting physical parameters from experimental and simulation data is presented. The method is based on statistical concepts and it relies on Monte Carlo simulation techniques. It identifies and determines with maximal…
We introduce a new Monte Carlo method by incorporating a guided distribution function to the conventional Monte Carlo method. In this way, the efficiency of Monte Carlo methods is drastically improved. To further speed up the algorithm, we…
Global optimization is an active area of research in atomistic simulations, and many algorithms have been proposed to date. A prominent example is basin hopping Monte Carlo, which performs a modified Metropolis Monte Carlo search to explore…
High-dimensional multimodal sampling problems from lattice field theory (LFT) have become important benchmarks for machine learning assisted sampling methods. We show that GPU-accelerated particle methods, Sequential Monte Carlo (SMC) and…
We describe an embarrassingly parallel, anytime Monte Carlo method for likelihood-free models. The algorithm starts with the view that the stochasticity of the pseudo-samples generated by the simulator can be controlled externally by a…