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We propose a new method for estimating rare event probabilities when independent samples are available. It is assumed that the underlying probability measures satisfy a large deviations principle with a scaling parameter $\varepsilon$ that…

Probability · Mathematics 2018-11-06 Paul Dupuis , Guo-Jhen Wu , Michael Snarski

We formulate the statistics of the discrete multicomponent fragmentation event using a methodology borrowed from statistical mechanics. We generate the ensemble of all feasible distributions that can be formed when a single integer…

Statistical Mechanics · Physics 2020-07-03 Themis Matsoukas

Rare events are events that are expected to occur infrequently, or more technically, those that have low probabilities (say, order of $10^{-3}$ or less) of occurring according to a probability model. In the context of uncertainty…

Computation · Statistics 2015-08-21 James L. Beck , Konstantin M. Zuev

In this work, we consider the numerical estimation of the probability for a stochastic process to hit a set B before reaching another set A. This event is assumed to be rare. We consider reactive trajectories of the stochastic Allen-Cahn…

Analysis of PDEs · Mathematics 2019-10-21 Charles-Edouard Bréhier , Maxime Gazeau , Ludovic Goudenège , Mathias Rousset

We present a new algorithm for approximate inference in probabilistic programs, based on a stochastic gradient for variational programs. This method is efficient without restrictions on the probabilistic program; it is particularly…

Machine Learning · Statistics 2013-01-08 David Wingate , Theophane Weber

We consider the problem of choosing design parameters to minimize the probability of an undesired rare event that is described through the average of $n$ iid random variables. Since the probability of interest for near optimal design…

Optimization and Control · Mathematics 2019-02-22 Amarjit Budhiraja , Shu Lu , Yang Yu , Quoc Tran-Dinh

Rare events play a key role in many applications and numerous algorithms have been proposed for estimating the probability of a rare event. However, relatively little is known on how to quantify the sensitivity of the probability with…

Probability · Mathematics 2019-02-06 Paul Dupuis , Markos A. Katsoulakis , Yannis Pantazis , Luc Rey-Bellet

We introduce and compare computational techniques for sharp extreme event probability estimates in stochastic differential equations with small additive Gaussian noise. In particular, we focus on strategies that are scalable, i.e. their…

Computation · Statistics 2023-11-27 Timo Schorlepp , Shanyin Tong , Tobias Grafke , Georg Stadler

We consider chance-constrained problems with discrete random distribution. We aim for problems with a large number of scenarios. We propose a novel method based on the stochastic gradient descent method which performs updates of the…

Optimization and Control · Mathematics 2019-05-28 Lukáš Adam , Martin Branda

We explore whether splitting and killing methods can improve the accuracy of Markov chain Monte Carlo (MCMC) estimates of rare event probabilities, and we make three contributions. First, we prove that "weighted ensemble" is the only…

Numerical Analysis · Mathematics 2020-12-17 Robert J. Webber , David Aristoff , Gideon Simpson

Multilevel Splitting is a Sequential Monte Carlo method to simulate realisations of a rare event as well as to estimate its probability. This article is concerned with the convergence and the fluctuation analysis of Adaptive Multilevel…

Statistics Theory · Mathematics 2015-09-21 Frederic Cerou , Arnaud Guyader

Improving Importance Sampling estimators for rare event probabilities requires sharp approx- imations of the optimal density leading to a nearly zero-variance estimator. This paper presents a new way to handle the estimation of the…

Statistics Theory · Mathematics 2014-01-15 Virgile Caron

When artificial neural networks have demonstrated exceptional practical success in a variety of domains, investigations into their theoretical characteristics, such as their approximation power, statistical properties, and generalization…

Machine Learning · Statistics 2023-10-06 Shijin Gong , Xinyu Zhang

We propose a class of strongly efficient rare event simulation estimators for random walks and compound Poisson processes with a regularly varying increment/jump-size distribution in a general large deviations regime. Our estimator is based…

Probability · Mathematics 2017-06-14 Bohan Chen , Jose Blanchet , Chang-Han Rhee , Bert Zwart

The paper presents a new efficient and robust method for rare event probability estimation for computational models of an engineering product or a process returning categorical information only, for example, either success or failure. For…

Computational Engineering, Finance, and Science · Computer Science 2022-10-11 Miroslav Vořechovský

We investigate sampling laws for particle algorithms and the influence of these laws on the efficiency of particle approximations of marginal likelihoods in hidden Markov models. Among a broad class of candidates we characterize the…

Computation · Statistics 2014-02-21 Nick Whiteley , Anthony Lee

Partial differential equation is a powerful tool to characterize various physics systems. In practice, measurement errors are often present and probability models are employed to account for such uncertainties. In this paper, we present a…

Probability · Mathematics 2016-05-23 Xiaoou Li , Jingchen Liu

Online prediction methods are typically presented as serial algorithms running on a single processor. However, in the age of web-scale prediction problems, it is increasingly common to encounter situations where a single processor cannot…

Machine Learning · Computer Science 2012-02-01 Ofer Dekel , Ran Gilad-Bachrach , Ohad Shamir , Lin Xiao

In this paper, we combine the operator splitting methodology for abstract evolution equations with that of stochastic methods for large-scale optimization problems. The combination results in a randomized splitting scheme, which in a given…

Numerical Analysis · Mathematics 2022-10-12 Monika Eisenmann , Tony Stillfjord

We revisit resampling procedures for error estimation in binary classification in terms of U-statistics. In particular, we exploit the fact that the error rate estimator involving all learning-testing splits is a U-statistic. Thus, it has…

Statistics Theory · Mathematics 2013-12-19 Mathias Fuchs , Roman Hornung , Riccardo De Bin , Anne-Laure Boulesteix