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

Authors:
Raúl Vicen-Bueno;M. Pilar Jarabo-Amores;Manuel Rosa-Zurera;José L. Sanz-González;Saturnino Maldonado-Bascón
Affiliations:
Signal Theory and Communications Department, Superior Polytechnic School, University of Alcalá, Alcalá de Henares, Madrid, Spain 28805;Signal Theory and Communications Department, Superior Polytechnic School, University of Alcalá, Alcalá de Henares, Madrid, Spain 28805;Signal Theory and Communications Department, Superior Polytechnic School, University of Alcalá, Alcalá de Henares, Madrid, Spain 28805;Signals, Systems and Radiocommunications Department, ETSI de Telecomunicación, Polytechnic University of Madrid, Madrid, Spain 28040;Signal Theory and Communications Department, Superior Polytechnic School, University of Alcalá, Alcalá de Henares, Madrid, Spain 28805
Venue:
Neural Processing Letters
Year:
2010

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Abstract

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.