Importance Splitting for Finite-Time Rare Event Simulation

Jiang, Guangxin; Fu, Michael C.

doi:10.1109/tac.2017.2758171

Cited by 5 publications

(3 citation statements)

References 31 publications

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“…e basic idea of the importance sampling method [33,34] is to change the probability density distribution of random variables, so as to obtain the samples of extremely small probability events with a higher probability. We now present the SMC method based on the importance sampling.…”

Section: Zero-variance Importance Sampling Distributionmentioning

confidence: 99%

“…However, the optimal importance sampling distribution obtained by the above method does not come from the distribution family of the system path space, and these methods actually belong to the heuristic importance sampling method. e importance segmentation method [34] is a method of reducing the estimated variance. Based on the importance segmentation method, J´egourel et al [33] proposed the SMC algorithm for the verification of small probability events.…”

Section: Related Workmentioning

confidence: 99%

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Towards a Statistical Model Checking Method for Safety-Critical Cyber-Physical System Verification

Xie

Tan

Fang

et al. 2021

Security and Communication Networks

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Safety-Critical Cyber-Physical System (SCCPS) refers to the system that if the system fails or its key functions fail, it will cause casualties, property damage, environmental damage, and other catastrophic consequences. Therefore, it is vital to verify the safety of safety critical systems. In the community, the SCCPS safety verification mainly relies on the statistical model checking methodology, but for SCCPS with extremely high safety requirements, the statistical model checking method is difficult/infeasible to sample the extremely small probability event since the probability of the system violating the safety is very low (rare property). In response to this problem, we propose a new method of statistical model checking for high-safety SCCPS. Firstly, with the CTMC-approximated SCCPS path probability space model, it leverages the maximum likelihood estimation method to learn the parameters of CTMC. Then, the embedded DTMC can be derived from CTMC, and a cross-entropy optimization model based on DTMC can be constructed. Finally, we propose an algorithm of iteratively learning the optimal importance sampling distribution on the discrete path space and an algorithm to check the statistical model of verifying the rare attribute. Eventually, experimental results show that the method proposed in this paper can effectively verify the rare attributes of SCCPS. Under the same sample size, comparing with the heuristic importance sampling methods, the estimated value of this method can be better distributed around the mean value, and the related standard deviation and relative error are reduced by more than an order of magnitude.

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Section: Zero-variance Importance Sampling Distributionmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Towards a Statistical Model Checking Method for Safety-Critical Cyber-Physical System Verification

Xie

Tan

Fang

et al. 2021

Security and Communication Networks

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“…Multilevel splitting methods have had many applications, such as the estimation of network reliability (Botev, L'Ecuyer, Rubino, Simard and Tuffin 2013) and of rare events in Jackson networks (Blanchet, Leder and Shi 2011). Multilevel splitting techniques for rare event simulation with finite time constraints are analysed in (Jiang and Fu 2017). A comprehensive survey on multilevel splitting techniques with applications to rare event simulations, sampling from complicated distributions, Monte Carlo counting, and randomized optimization, can be found in (Rubinstein and Kroese 2016, Ch.…”

Section: Introductionmentioning

confidence: 99%

Randomized Dimension Reduction for Monte Carlo Simulations

Kahale

2020

Management Science

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We present a new unbiased algorithm that estimates the expected value of f (U ) via Monte Carlo simulation, where U is a vector of d independent random variables, and f is a function of d variables. We assume that f does not depend equally on all its arguments. Under certain conditions we prove that, for the same computational cost, the variance of our estimator is lower than the variance of the standard Monte Carlo estimator by a factor of order d. Our method can be used to obtain a low-variance unbiased estimator for the expectation of a function of the state of a Markov chain at a given time-step. We study applications to volatility forecasting and time-varying queues. Numerical experiments show that our algorithm dramatically improves upon the standard Monte Carlo method for large values of d, and is highly resilient to discontinuities.

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