5,282 research outputs found
Bounding rare event probabilities in computer experiments
We are interested in bounding probabilities of rare events in the context of
computer experiments. These rare events depend on the output of a physical
model with random input variables. Since the model is only known through an
expensive black box function, standard efficient Monte Carlo methods designed
for rare events cannot be used. We then propose a strategy to deal with this
difficulty based on importance sampling methods. This proposal relies on
Kriging metamodeling and is able to achieve sharp upper confidence bounds on
the rare event probabilities. The variability due to the Kriging metamodeling
step is properly taken into account. The proposed methodology is applied to a
toy example and compared to more standard Bayesian bounds. Finally, a
challenging real case study is analyzed. It consists of finding an upper bound
of the probability that the trajectory of an airborne load will collide with
the aircraft that has released it.Comment: 21 pages, 6 figure
Techniques for the Fast Simulation of Models of Highly dependable Systems
With the ever-increasing complexity and requirements of highly dependable systems, their evaluation during design and operation is becoming more crucial. Realistic models of such systems are often not amenable to analysis using conventional analytic or numerical methods. Therefore, analysts and designers turn to simulation to evaluate these models. However, accurate estimation of dependability measures of these models requires that the simulation frequently observes system failures, which are rare events in highly dependable systems. This renders ordinary Simulation impractical for evaluating such systems. To overcome this problem, simulation techniques based on importance sampling have been developed, and are very effective in certain settings. When importance sampling works well, simulation run lengths can be reduced by several orders of magnitude when estimating transient as well as steady-state dependability measures. This paper reviews some of the importance-sampling techniques that have been developed in recent years to estimate dependability measures efficiently in Markov and nonMarkov models of highly dependable system
Temperature Overloads in Power Grids Under Uncertainty: a Large Deviations Approach
The advent of renewable energy has huge implications for the design and
control of power grids. Due to increasing supply-side uncertainty, traditional
reliability constraints such as strict bounds on current, voltage and
temperature in a transmission line have to be replaced by computationally
demanding chance constraints. In this paper we use large deviations techniques
to study the probability of current and temperature overloads in power grids
with stochastic power injections, and develop corresponding safe capacity
regions. In particular, we characterize the set of admissible power injections
such that the probability of overloading of any line over a given time interval
stays below a fixed target. We show how enforcing (stochastic) constraints on
temperature, rather than on current, results in a less conservative approach
and can thus lead to capacity gains.Comment: 12 pages (10 pages + 2 pages appendix), 2 figures. Revised version
with extended numerical sectio
Lung Nodule Classification by the Combination of Fusion Classifier and Cascaded Convolutional Neural Networks
Lung nodule classification is a class imbalanced problem, as nodules are
found with much lower frequency than non-nodules. In the class imbalanced
problem, conventional classifiers tend to be overwhelmed by the majority class
and ignore the minority class. We showed that cascaded convolutional neural
networks can classify the nodule candidates precisely for a class imbalanced
nodule candidate data set in our previous study. In this paper, we propose
Fusion classifier in conjunction with the cascaded convolutional neural network
models. To fuse the models, nodule probabilities are calculated by using the
convolutional neural network models at first. Then, Fusion classifier is
trained and tested by the nodule probabilities. The proposed method achieved
the sensitivity of 94.4% and 95.9% at 4 and 8 false positives per scan in Free
Receiver Operating Characteristics (FROC) curve analysis, respectively.Comment: Draft of ISBI2018. arXiv admin note: text overlap with
arXiv:1703.0031
Bayesian subset simulation
We consider the problem of estimating a probability of failure ,
defined as the volume of the excursion set of a function above a given threshold, under a given
probability measure on . In this article, we combine the popular
subset simulation algorithm (Au and Beck, Probab. Eng. Mech. 2001) and our
sequential Bayesian approach for the estimation of a probability of failure
(Bect, Ginsbourger, Li, Picheny and Vazquez, Stat. Comput. 2012). This makes it
possible to estimate when the number of evaluations of is very
limited and is very small. The resulting algorithm is called Bayesian
subset simulation (BSS). A key idea, as in the subset simulation algorithm, is
to estimate the probabilities of a sequence of excursion sets of above
intermediate thresholds, using a sequential Monte Carlo (SMC) approach. A
Gaussian process prior on is used to define the sequence of densities
targeted by the SMC algorithm, and drive the selection of evaluation points of
to estimate the intermediate probabilities. Adaptive procedures are
proposed to determine the intermediate thresholds and the number of evaluations
to be carried out at each stage of the algorithm. Numerical experiments
illustrate that BSS achieves significant savings in the number of function
evaluations with respect to other Monte Carlo approaches
Quantum Sampling Problems, BosonSampling and Quantum Supremacy
There is a large body of evidence for the potential of greater computational
power using information carriers that are quantum mechanical over those
governed by the laws of classical mechanics. But the question of the exact
nature of the power contributed by quantum mechanics remains only partially
answered. Furthermore, there exists doubt over the practicality of achieving a
large enough quantum computation that definitively demonstrates quantum
supremacy. Recently the study of computational problems that produce samples
from probability distributions has added to both our understanding of the power
of quantum algorithms and lowered the requirements for demonstration of fast
quantum algorithms. The proposed quantum sampling problems do not require a
quantum computer capable of universal operations and also permit physically
realistic errors in their operation. This is an encouraging step towards an
experimental demonstration of quantum algorithmic supremacy. In this paper, we
will review sampling problems and the arguments that have been used to deduce
when sampling problems are hard for classical computers to simulate. Two
classes of quantum sampling problems that demonstrate the supremacy of quantum
algorithms are BosonSampling and IQP Sampling. We will present the details of
these classes and recent experimental progress towards demonstrating quantum
supremacy in BosonSampling.Comment: Survey paper first submitted for publication in October 2016. 10
pages, 4 figures, 1 tabl
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