Introduction to importance sampling in rare-event simulations

Denny, Mark

doi:10.1088/0143-0807/22/4/315

Cited by 70 publications

(33 citation statements)

References 4 publications

(10 reference statements)

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“…Thus, in [8], a stochastic gradient learning algorithm based on IS techniques for unsupervised learning of over-complete dictionaries is presented. As in the previous works [1][2][3][4][5][6][7], it is shown in [8] that the proposed algorithm is faster and more efficient than classical ones. Moreover, its great efficiency allows the treatment of large-scale problems in a statistically sound framework, as demonstrated for the extraction of individual piano notes from a polyphonic piano recording.…”

Section: Introductionmentioning

confidence: 52%

“…, N , are independent sample vectors whose pdf's are f * x (x) (this pdf is known as the Importance Sampling pdf or the biasing pdf). The estimatorÊ * , given by (3), must be computed in order to perform the NN training, i.e., in order to find the NN parameters that minimize the objective function E.…”

Section: Importance Sampling Techniquementioning

confidence: 99%

“…In this way, some limitations of the Monte Carlo simulation for some functional spaces that define the regularity of the input data are exposed in [1]. Nevertheless, an accurate estimation of a process or function can be achieved by the use of importance sampling (IS) techniques [2,3]. These techniques have been successfully applied in different kind of learning structures.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Importance Sampling for Objective Function Estimations in Neural Detector Training Driven by Genetic Algorithms

Vicen-Bueno

Jarabo-Amores

Rosa-Zurera

et al. 2010

Neural Process Lett

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To train Neural Networks (NNs) in a supervised way, estimations of an objective function must be carried out. The value of this function decreases as the training progresses and so, the number of test observations necessary for an accurate estimation has to be increased. Consequently, the training computational cost is unaffordable for very low objective function value estimations, and the use of Importance Sampling (IS) techniques becomes convenient. The study of three different objective functions is considered, which implies the proposal of estimators of the objective function using IS techniques: the Mean-Square error, the Cross Entropy error and the Misclassification error criteria. The values of these functions are estimated by IS techniques, and the results are used to train NNs by the application of Genetic Algorithms. Results for a binary detection in Gaussian noise are provided. These results show the evolution of the parameters during the training and the performances of the proposed detectors in terms of error probability and Receiver Operating Characteristics curves. At the end of the study, the obtained results justify the convenience of using IS in the training.

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Section: Introductionmentioning

confidence: 52%

Section: Importance Sampling Techniquementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Importance Sampling for Objective Function Estimations in Neural Detector Training Driven by Genetic Algorithms

Vicen-Bueno

Jarabo-Amores

Rosa-Zurera

et al. 2010

Neural Process Lett

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“…The posterior probability density P (σ|D) for the signal cross section σ given the observed number of events D is obtained by integration over the parameters a and b The technical implementation is realized within the package top statistics [161], [162]. Monte Carlo importance sampling [163] is used for the numerical integration Eq. 8.…”

Section: Binned Likelihood Methodsmentioning

confidence: 99%

Search for new heavy charged gauge bosons

Magass¹,

Hebbeker²

2007

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Additional gauge bosons are introduced in many theoretical extensions to the Standard Model. A search for a new heavy charged gauge boson W ′ decaying into an electron and a neutrino is presented. The data used in this analysis was taken with the DØ detector at the Fermilab proton-antiproton collider at a center-of-mass energy of 1.96 TeV and corresponds to an integrated luminosity of about 1 fb −1 . Since no significant excess is observed in the data, an upper limit is set on the production cross section times branching fraction σ W ′ ×Br (W ′ → eν). Using this limit, a W ′ boson with mass below ∼1 TeV can be excluded at the 95% confidence level assuming that the new boson has the same couplings to fermions as the Standard Model W boson. Search for New Heavy Charged Gauge BosonsAdditional gauge bosons (including the equivalent to the Z, the Z ′ ) are introduced in many extensions to the Standard Model of particle physics. Assuming the most general case, the new gauge group can comprise a new mixing angle and new couplings. Here, the Altarelli Reference Model is considered which represents a generalization of the Manifest Left-Right Symmetric Model with light right-handed neutrinos. This model makes the assumptions that the new gauge boson W ′ has the same couplings as the Standard Model W boson and that there is no mixing. Hence, the W ′ is a heavy copy of the Standard Model W boson.The clear decay signature (in analogy to the decay of the W ) contains an isolated electron with extreme high energy which is important for triggering. The neutrino can not be detected, but it gives rise to missing energy in the detector. The Jacobian peak in the transverse mass distribution stemming from the W decay is used for calibration, whereas the tail of the transverse mass distribution is searched for a possible W ′ signal.The data agrees with the expectation from background processes. For instance, in the data 37 events are reconstructed with transverse masses above 300 GeV compared to a prediction of 37.1 ± 2.1 (stat) +6.0 −3.7 (sys) background events. Since no significant excess is found in the data, an upper limit is set on the production cross section for heavy charged gauge bosons decaying into electron and neutrino, σ W ′ × Br (W ′ → eν). Using this limit, a lower bound on the mass of the new gauge boson can be derived at the 95% confidence level,

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“…Therefore, it is of great interest to study the probabilistic distribution of node voltageBL at the end time step of reading operation considering the process variations. Note that the reading failure of SRAM bit cell is a "rare event" with extremely small probability [27] that is not in the scope of this paper, while the overall stochastic discharge behavior in this SRAM cell will be studied.…”

Section: A 6-t Sram Bit Cellmentioning

confidence: 99%

Stochastic Behavioral Modeling and Analysis for Analog/Mixed-Signal Circuits

Gong

Basir-Kazeruni

et al. 2013

IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst.

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Abstract-It has become increasingly challenging to model the stochastic behavior of analog/mixed-signal (AMS) circuits under large-scale process variations. In this paper, a novel momentmatching-based method has been proposed to accurately extract the probabilistic behavioral distributions of AMS circuits. This method first utilizes Latin hypercube sampling coupling with a correlation control technique to generate a few samples (e.g., sample size is linear with number of variable parameters) and further analytically evaluate the high-order moments of the circuit behavior with high accuracy. In this way, the arbitrary probabilistic distributions of the circuit behavior can be extracted using moment-matching method. More importantly, the proposed method has been successfully applied to high-dimensional problems with linear complexity. The experiments demonstrate that the proposed method can provide up to 1666X speedup over crude Monte Carlo method for the same accuracy.

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Introduction to importance sampling in rare-event simulations

Cited by 70 publications

References 4 publications

Importance Sampling for Objective Function Estimations in Neural Detector Training Driven by Genetic Algorithms

Importance Sampling for Objective Function Estimations in Neural Detector Training Driven by Genetic Algorithms

Search for new heavy charged gauge bosons

Stochastic Behavioral Modeling and Analysis for Analog/Mixed-Signal Circuits

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