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The effectiveness of stochastic algorithms based on Monte Carlo dynamics in solving hard optimization problems is mostly unknown. Beyond the basic statement that at a dynamical phase transition the ergodicity breaks and a Monte Carlo…

Disordered Systems and Neural Networks · Physics 2019-07-10 Maria Chiara Angelini , Federico Ricci-Tersenghi

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…

Computation · Statistics 2018-09-28 Bochao Jia

For real symmetric matrices that are accessible only through matrix vector products, we present Monte Carlo estimators for computing the diagonal elements. Our probabilistic bounds for normwise absolute and relative errors apply to Monte…

Numerical Analysis · Mathematics 2022-03-18 Eric Hallman , Ilse C. F. Ipsen , Arvind Saibaba

In dynamic Monte Carlo simulations, using for example the Metropolis dynamic, it is often required to simulate for long times and to simulate large systems. We present an overview of advanced algorithms to simulate for larger times and to…

Statistical Mechanics · Physics 2007-05-23 M. A. Novotny , Alice K. Kolakowska , G. Korniss

In many problems, complex non-Gaussian and/or nonlinear models are required to accurately describe a physical system of interest. In such cases, Monte Carlo algorithms are remarkably flexible and extremely powerful approaches to solve such…

Computation · Statistics 2015-04-23 Thi Le Thu Nguyen , Francois Septier , Gareth W. Peters , Yves Delignon

We analyse a multilevel Monte Carlo method for the approximation of distribution functions of univariate random variables. Since, by assumption, the target distribution is not known explicitly, approximations have to be used. We provide an…

Probability · Mathematics 2017-06-22 Mike B. Giles , Tigran Nagapetyan , Klaus Ritter

A quantum Monte Carlo algorithm for the transverse Ising model with arbitrary short- or long-range interactions is presented. The algorithm is based on sampling the diagonal matrix elements of the power series expansion of the density…

Statistical Mechanics · Physics 2007-05-23 Anders W. Sandvik

We present a general framework for accelerating a large class of widely used Markov chain Monte Carlo (MCMC) algorithms. Our approach exploits fast, iterative approximations to the target density to speculatively evaluate many potential…

Machine Learning · Statistics 2014-03-31 Elaine Angelino , Eddie Kohler , Amos Waterland , Margo Seltzer , Ryan P. Adams

We design and implement a novel algorithm for computing a multilevel Monte Carlo (MLMC) estimator of the cumulative distribution function of a quantity of interest in problems with random input parameters or initial conditions. Our approach…

Numerical Analysis · Mathematics 2020-08-26 Søren Taverniers , Daniel M. Tartakovsky

The use of sparse precision (inverse covariance) matrices has become popular because they allow for efficient algorithms for joint inference in high-dimensional models. Many applications require the computation of certain elements of the…

Computation · Statistics 2017-12-06 Per Sidén , Finn Lindgren , David Bolin , Mattias Villani

We present a matrix factorization algorithm that scales to input matrices that are large in both dimensions (i.e., that contains morethan 1TB of data). The algorithm streams the matrix columns while subsampling them, resulting in low…

Optimization and Control · Mathematics 2016-12-04 Arthur Mensch , Julien Mairal , Gaël Varoquaux , Bertrand Thirion

Markov Chain Monte Carlo (MCMC) is a well-established family of algorithms primarily used in Bayesian statistics to sample from a target distribution when direct sampling is challenging. Existing work on Bayesian decision trees uses MCMC.…

Computation · Statistics 2023-01-24 Efthyvoulos Drousiotis , Paul G. Spirakis , Simon Maskell

Selecting a good column (or row) subset of massive data matrices has found many applications in data analysis and machine learning. We propose a new adaptive sampling algorithm that can be used to improve any relative-error column selection…

Data Structures and Algorithms · Computer Science 2015-10-15 Saurabh Paul , Malik Magdon-Ismail , Petros Drineas

We introduce a powerful and flexible MCMC algorithm for stochastic simulation. The method builds on a pseudo-marginal method originally introduced in [Genetics 164 (2003) 1139--1160], showing how algorithms which are approximations to an…

Statistics Theory · Mathematics 2009-04-01 Christophe Andrieu , Gareth O. Roberts

The purpose of this text is to provide an accessible introduction to a set of recently developed algorithms for factorizing matrices. These new algorithms attain high practical speed by reducing the dimensionality of intermediate…

Numerical Analysis · Mathematics 2019-02-08 Per-Gunnar Martinsson

A Monte Carlo algorithm is said to be adaptive if it automatically calibrates its current proposal distribution using past simulations. The choice of the parametric family that defines the set of proposal distributions is critical for good…

Statistics Theory · Mathematics 2011-11-11 Christian Schäfer , Nicolas Chopin

A number of algorithms have been developed to solve probabilistic inference problems on belief networks. These algorithms can be divided into two main groups: exact techniques which exploit the conditional independence revealed when the…

Artificial Intelligence · Computer Science 2013-04-08 Ross D. Shachter , Mark Alan Peot

As it has become common to use many computer cores in routine applications, finding good ways to parallelize popular algorithms has become increasingly important. In this paper, we present a parallelization scheme for Markov chain Monte…

Methodology · Statistics 2016-06-01 Guillaume W. Basse , Natesh S. Pillai , Aaron Smith

While recent work towards the development of tight-binding and ab-initio algorithms has focused on molecular dynamics, Monte Carlo methods can often lead to better results with relatively little effort. We present here a multi-step Monte…

Statistical Mechanics · Physics 2009-10-31 Parthapratim Biswas , G. T. Barkema , Normand Mousseau , W. F. van der Weg

Adaptive Monte Carlo methods are very efficient techniques designed to tune simulation estimators on-line. In this work, we present an alternative to stochastic approximation to tune the optimal change of measure in the context of…

Probability · Mathematics 2009-10-23 Benjamin Jourdain , Jérôme Lelong