A comparison of criterion functions for a neural network applied to binary detection

Andina, Diego; Sanz-González, J.L.; Jimenez-Pajares, J.A.

doi:10.1109/icnn.1995.488119

Cited by 14 publications

(11 citation statements)

References 7 publications

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“…To illustrate the use of IS techniques in the training phase of a NN, let us consider the misclassification probability as an objective function for applications in classifications (or the error probability for detection in communications [11][12][13]). According to the notation given above, the error probability (P e ) can be expressed as follows…”

Section: Fig 1 Binary Detector Structure 2 Error Probability As Objmentioning

confidence: 99%

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Importance Sampling Techniques in Neural Detector Training

Sanz-González

Andina

2001

Machine Learning: ECML 2001

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Importance Sampling is a modified Monte Carlo technique applied to the estimation of rare event probabilities (very low probabilities). In this paper, we propose and develop the use of Importance Sampling (IS) techniques in neural network training, for applications to detection in communication systems. Some key topics are introduced, such as modifications of the error probability objective function, optimal and suboptimal IS probability density functions (biasing density functions), and experimental results of training with a genetic algorithm. Also, it is shown that the genetic algorithm with the IS technique attains quasi-optimum training in the sense of minimum error probability (or minimum misclassification probability).

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Section: Fig 1 Binary Detector Structure 2 Error Probability As Objmentioning

confidence: 99%

“…depends on a parameter q (e.g. the signal-to-noise ratio) [12,13] and we can write (11) where q * is the q-value that minimizes the variance (6) of the estimator The optimal q * -value is obtained experimentally by computing an estimator of (6). An estimator of (6) is given by…”

Section: Fig 1 Binary Detector Structure 2 Error Probability As Objmentioning

confidence: 99%

Importance Sampling Techniques in Neural Detector Training

Sanz-González

Andina

2001

Machine Learning: ECML 2001

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“…Gandhi et al [4,5] and J.L. Sanz and D. Andina [6,7] applied multilayer perceptrons with one output to approximate the Neyman-Pearson detector. Once the neural network had been trained, they proposed to vary the detection threshold attending to P F A requirements.…”

Section: Introductionmentioning

confidence: 99%

“…Once the neural network had been trained, they proposed to vary the detection threshold attending to P F A requirements. In [4,5] the LMSE criterion was used, while in [6,7] the LMSE and cross-entropy errors were used, among others. For desired outputs 1 for hypothesis H 1 and 0 for hypothesis H 0 , their works are based on the assumption that the network converges to an "operating point" that minimizes the probability of error over the training set.…”

Section: Introductionmentioning

confidence: 99%

Sufficient condition for an adaptive system to approximate the Neyman-Pearson detector

Jarabo-Amores

Rosa-Zurera

Gil-Pita

et al. 2005

IEEE/SP 13th Workshop on Statistical Signal Processing, 2005

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The application of adaptive systems to approximate the Neyman-Pearson detector is considered. The training error function is proved to be the key parameter that determines the possibility of approximating this detector. Based on the calculus of the approximated function for the selected error criterion, a sufficient condition is derived. Decision rules based on expressions of the optimum Bayes discriminant function, such as those approximated for the LMSE or the cross-entropy error criteria, have been analyzed. Previous works were based on the assumption that the system was trained to minimize the probability of error over the training set, so its performance was only optimal for the minimum probability of error threshold (system "operating point"). In this work, we prove that the decision rule based on the function approximated for an error function that fulfil the derived sufficient condition is optimum for all possible P F A values. So, the concept of "operating point" will have no sense.

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“…The threshold is used to fix the desired P FA . This scheme has been used previously is several works [1,[18][19][20]. An equivalent implementation consist in varying the bias of the output neuron [21,22].…”

Section: Introductionmentioning

confidence: 99%

Radar detection with the Neyman–Pearson criterion using supervised-learning-machines trained with the cross-entropy error

Jarabo-Amores

Mata-Moya

Gil-Pita

et al. 2013

EURASIP J. Adv. Signal Process.

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The application of supervised learning machines trained to minimize the Cross-Entropy error to radar detection is explored in this article. The detector is implemented with a learning machine that implements a discriminant function, which output is compared to a threshold selected to fix a desired probability of false alarm. The study is based on the calculation of the function the learning machine approximates to during training, and the application of a sufficient condition for a discriminant function to be used to approximate the optimum Neyman-Pearson (NP) detector. In this article, the function a supervised learning machine approximates to after being trained to minimize the Cross-Entropy error is obtained. This discriminant function can be used to implement the NP detector, which maximizes the probability of detection, maintaining the probability of false alarm below or equal to a predefined value. Some experiments about signal detection using neural networks are also presented to test the validity of the study.

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A comparison of criterion functions for a neural network applied to binary detection

Cited by 14 publications

References 7 publications

Importance Sampling Techniques in Neural Detector Training

Importance Sampling Techniques in Neural Detector Training

Sufficient condition for an adaptive system to approximate the Neyman-Pearson detector

Radar detection with the Neyman–Pearson criterion using supervised-learning-machines trained with the cross-entropy error

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