Study of Two Error Functions to Approximate the Neyman–Pearson Detector Using Supervised Learning Machines

Jarabo-Amores, María-Pilar; Rosa-Zurera, Manuel; Gil-Pita, Roberto; López-Ferreras, F.

doi:10.1109/tsp.2009.2025077

Cited by 32 publications

(24 citation statements)

References 31 publications

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“…In this article, an extension of the theoretical study presented in [1] about the capability of supervised learning machines to approximate the Neyman-Pearson (NP) detector is presented. This detector can be implemented by comparing the likelihood ratio, (z), to a detection threshold fixed taking into account Probability of False Alarm (P FA ) requirements, as stated in expression (1) [2,3], being f (z|H i ), i ∈ {0, 1}, the likelihood functions under both, the null (H 0 ) and the alternative (H 1 ) hypothesis.…”

Section: Introductionmentioning

confidence: 99%

“…This detector can be implemented by comparing the likelihood ratio, (z), to a detection threshold fixed taking into account Probability of False Alarm (P FA ) requirements, as stated in expression (1) [2,3], being f (z|H i ), i ∈ {0, 1}, the likelihood functions under both, the null (H 0 ) and the alternative (H 1 ) hypothesis.…”

Section: Introductionmentioning

confidence: 99%

“…The usage of learning machines based detectors, allows us to approximate the NP detector, just using training data obtained experimentally, without knowledge of the likelihood functions. The main advantage of this approach is that no statistical models have to be assumed during the design, and if a suitable error function is used during training, a good approximation to the optimal NP detector http://asp.eurasipjournals.com/content/2013/1/44 is obtained [1]. The main drawback is the difficulty of obtaining representative training samples, and the definition of the most suitable learning machine architecture.…”

Section: Introductionmentioning

confidence: 99%

“…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%

“…A sufficient condition for a discriminant function to be suitable for implementing the NP detector was obtained. In [1], those results were used to carry out a more general study about the capability of learning machines to approximate the NP detector when they are trained in a supervised manner to minimize an error function, demonstrating that the Sum-of-Squares error is suitable to approximate the NP detector, and the Minkowski error with R = 1 is suitable to approximate the minimum probability of error classifier. With R = 1, the Minkowski error reduces to the mean absolute deviation.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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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SONN and MLP Based Solutions for Detecting Fluctuating Targets with Unknown Doppler Shift in Gaussian Interference

Mata-Moya

Jarabo-Amores

del-Rey-Maestre

et al. 2013

Advances in Computational Intelligence

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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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Study of Two Error Functions to Approximate the Neyman–Pearson Detector Using Supervised Learning Machines

Cited by 32 publications

References 31 publications

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

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

SONN and MLP Based Solutions for Detecting Fluctuating Targets with Unknown Doppler Shift in Gaussian Interference

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

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