Elements of Importance Sampling

In this paper we address the problem of verifying in stochastic hybrid systems temporal logic properties whose probability of being true is very small -rare events. It is well known that sampling-based (Monte Carlo) techniques, such as statistical model checking, do not perform well for estimating rare-event probabilities. The problem is that the sample size required for good accuracy grows too large as the event probability tends to zero. However, several techniques have been developed to address this problem. We focus on importance sampling techniques, which bias the original system to compute highly accurate and efficient estimates. The main difficulty in importance sampling is to devise a good biasing density, that is, a density yielding a low-variance estimator. In this paper, we show how to use the cross-entropy method for generating approximately optimal biasing densities for statistical model checking. We apply the method with importance sampling and statistical model checking for estimating rare-event probabilities in stochastic hybrid systems coded as Stateflow/Simulink diagrams.

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“…Here we present a brief overview of the technique -the interested reader can find more details in [15], for example.…”

Section: Importance Samplingmentioning

confidence: 99%

“…For completeness, we report some standard results about importance sampling [15] and the cross-entropy [12].…”

Section: Appendixmentioning

confidence: 99%

Rare-event verification for stochastic hybrid systems

Zuliani

Baier

Clarke

2012

Proceedings of the 15th ACM International Conference on Hybrid Systems: Computation and Control

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“…It has been shown that importance sampling method can reduce and even eliminate variation if an appropriate alternative distribution is found [15], [16]. This can be shown on the example illustrated in Figure 1.…”

Section: Introductionmentioning

confidence: 93%

Fast and Accurate DPPM Computation Using Model Based Filtering

Yılmaz

Ozev

2011

2011 Sixteenth IEEE European Test Symposium

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Defective Parts Per Million (DPPM) is an important quality metric that indicates the ratio of defective devices shipped to the customers. It is necessary to estimate and minimize DPPM in order to meet the desired level of quality. However, DPPM estimation requires statistical simulations, which are computationally costly if traditional methods are used. In this work, we propose an efficient DPPM estimation method for analog circuits that greatly reduces the computational burden. We employ a model based approach to selectively simulate only consequential samples in DPPM estimation. We include methods to mitigate the effect of model imperfection and robust model fitting to guarantee a consistent and efficient estimation. Experimental results show that the proposed method achieves 10x to 25x reduction in the number of simulations for an RF receiver front-end circuit.

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“…We develop our multifidelity approach in the context of the computation of failure probabilities [2,3] with the Monte Carlo method and importance sampling [4,5,6]. Failure probabilities are typically small and thus the Monte Carlo method requires many model evaluations to derive an accurate estimate.…”

Section: Introductionmentioning

confidence: 99%

“…In the second step, samples are drawn from the biasing distribution to derive an estimate of the failure probability. The key challenge is to construct an effective biasing distribution that leads to many samples for which a failure event occurs [4,6]. Several approaches for constructing a biasing distribution have been presented.…”

Section: Introductionmentioning

confidence: 99%

Multifidelity importance sampling

Peherstorfer

Cui

Marzouk

et al. 2016

Computer Methods in Applied Mechanics and Engineering

118

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Estimating statistics of model outputs with the Monte Carlo method often requires a large number of model evaluations. This leads to long runtimes if the model is expensive to evaluate. Importance sampling is one approach that can lead to a reduction in the number of model evaluations. Importance sampling uses a biasing distribution to sample the model more efficiently, but generating such a biasing distribution can be difficult and usually also requires model evaluations. A different strategy to speed up Monte Carlo sampling is to replace the computationally expensive high-fidelity model with a computationally cheap surrogate model; however, because the surrogate model outputs are only approximations of the high-fidelity model outputs, the estimate obtained using a surrogate model is in general biased with respect to the estimate obtained using the high-fidelity model. We introduce a multifidelity importance sampling (MFIS) method, which combines evaluations of both the high-fidelity and a surrogate model. It uses a surrogate model to facilitate the construction of the biasing distribution, but relies on a small number of evaluations of the high-fidelity model to derive an unbiased estimate of the statistics of interest. We prove that the MFIS estimate is unbiased even in the absence of accuracy guarantees on the surrogate model itself. The MFIS method can be used with any type of surrogate model, such as projection-based reduced-order models and data-fit models. Furthermore, the MFIS method is applicable to black-box models, i.e., where only inputs and the corresponding outputs of the high-fidelity and the surrogate model are available but not the details of the models themselves. We demonstrate on nonlinear and time-dependent problems that our MFIS method achieves speedups of up to several orders of magnitude compared to Monte Carlo with importance sampling that uses the high-fidelity model only.

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Elements of Importance Sampling

Cited by 6 publications

References 0 publications

Rare-event verification for stochastic hybrid systems

Rare-event verification for stochastic hybrid systems

Fast and Accurate DPPM Computation Using Model Based Filtering

Multifidelity importance sampling

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