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

Vicen-Bueno, R.; Jarabo-Amores, María-Pilar; Rosa-Zurera, Manuel; Sanz-González, J.L.; Maldonado-Bascón, Saturnino

doi:10.1007/s11063-010-9155-8

Cited by 3 publications

(3 citation statements)

References 30 publications

(55 reference statements)

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“…In fact, the variance

σ_{{\hat{P}}_{0}}^{2}

{\hat{P}}_{0}

σ_{{\hat{P}}_{0}}^{2} = E^{*} (}{, {({\overset{false^}{P}}_{0} - P_{0})}^{2}) = \frac{1}{N} (E^{*} \{{(][, w_{bold-italicX} false(X false) \cdot u ()(, t false(X false) - t_{0}))}^{2}\} - P_{0}^{2})

As is well‐known [1],

f_{bold-italicX}^{*} false(x false) = f_{bold-italicX} false(x false) \cdot u ()(, t false(x false) - t_{0}) / P_{0}

provides zero variance in (2) for any N ≥ 1; however, it is not practical because P 0 is unknown (in fact, it has to be estimated). In the literature [1–4], some families of

f_{bold-italicX}^{*} false(x false)

have been proposed for different estimation problems and the optimal solution is constrained to this family.…”

Section: Introductionmentioning

confidence: 99%

“…Introduction: As is well-known, the importance sampling (IS) technique [1][2][3][4] is a modified Monte-Carlo simulation applied to rare-event probability estimation, such as estimation of very low false-alarm probability in radar detection, or very low error-probability in communications.…”

mentioning

confidence: 99%

“…As is well-known [1], f * X (x) = f X (x) • u t(x) − t 0 /P 0 provides zero variance in (2) for any N ≥ 1; however, it is not practical because P 0 is unknown (in fact, it has to be estimated). In the literature [1][2][3][4], some families of f * X (x) have been proposed for different estimation problems and the optimal solution is constrained to this family.…”

mentioning

confidence: 99%

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Reducing dimensionality effect in importance sampling simulations

2013

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The dimensionality effect is avoided by the use of sufficient statistics in event probability estimators realised by importance sampling. If the system function is not a sufficient statistic, an approach is proposed to reduce the dimensionality effect in the estimators. Simulation results of false-alarm probability estimations, applied to radar detection, confirm a clear concordance with the theoretical results.

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“…In fact, the variance

σ_{{\hat{P}}_{0}}^{2}

{\hat{P}}_{0}

σ_{{\hat{P}}_{0}}^{2} = E^{*} (}{, {({\overset{false^}{P}}_{0} - P_{0})}^{2}) = \frac{1}{N} (E^{*} \{{(][, w_{bold-italicX} false(X false) \cdot u ()(, t false(X false) - t_{0}))}^{2}\} - P_{0}^{2})

As is well‐known [1],

f_{bold-italicX}^{*} false(x false) = f_{bold-italicX} false(x false) \cdot u ()(, t false(x false) - t_{0}) / P_{0}

provides zero variance in (2) for any N ≥ 1; however, it is not practical because P 0 is unknown (in fact, it has to be estimated). In the literature [1–4], some families of