Skip to main content

Advertisement

SpringerLink
Log in

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

  • Published:
Neural Processing Letters Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Atanassov E, Dimov IT (2007) What Monte Carlo models can do and cannot do efficiently?. Appl Math Model 32: 1477–1500

    Article  MathSciNet  Google Scholar 

  2. Borcherds PH (2000) Importance sampling: an illustrative introduction. Eur J Phys 21: 405–411

    Article  Google Scholar 

  3. Denny M (2001) Introduction to importance sampling in rare-event simulations. Eur J Phys 22: 403–411

    Article  Google Scholar 

  4. Andrieu C, Freitas N, Doucet A, Jordan MI (2003) An introduction to MCMC for machine learning. Mach Learn 50: 5–43

    Article  MATH  Google Scholar 

  5. Bengio Y, Senécal JS (2003) Quick training of probabilistic neural nets by importance sampling. In: Proceedings of artificial intelligence statistics 2003 (AIStats 2003)

  6. Bengio Y, Senécal JS (2008) Adaptive importance sampling to accelerate training of a neural probabilistic language model. IEEE Trans Neural Netw 19: 713–722

    Article  Google Scholar 

  7. Yuan C, Druzdzel MJ (2006) Importance sampling algorithms for Bayesian networks: principles and performance. Math Comput Model 43: 1189–1207

    Article  MATH  MathSciNet  Google Scholar 

  8. Blumensath T, Davies M (2005) A fast importance sampling algorithm for unsupervised learning of over-complete dictionaries. In: Proceedings of the IEEE international conference on acoustics, speech, and signal processing, 2005 (ICASSP ‘05), March 18–23, vol 5, pp 213–216

  9. Uchibe E, Doya K (2004) Competitive-cooperative-concurrent reinforcement learning with importance sampling. In: Proceedings of the 8th international conference on simulation of adaptive behavior: from animals and animats, July 13–17, pp 287–296

  10. Chen JC, Lu D, Sadowsky JS, Yao K (1993) On importance sampling in digital communications. Part I: fundamentals. IEEE J Sel Areas Commun 11: 289–299

    Article  Google Scholar 

  11. Wolfe RJ, Jeruchim MC, Hahn PM (1990) On optimum and suboptimum biasing procedures for importance sampling in communication simulation. IEEE Trans Commun 38: 639–647

    Article  Google Scholar 

  12. Al-Qaq WA, Devetsikiotis M, Townsend JK (1995) Stochastic gradient optimization of importance sampling for the efficient simulation of digital communication systems. IEEE Trans Commun 43: 2975–2985

    Article  Google Scholar 

  13. Smith PJ, Shafi M, Gao H (1997) Quick simulation: a review of importance sampling techniques in communications systems. IEEE J Sel Areas Commun 15: 597–613

    Article  Google Scholar 

  14. Al-Qaq WA, Townsend JK (1997) A stochastic importance sampling methodology for the efficient simulation of adaptive systems in frequency nonselective Rayleigh fading channels. IEEE J Sel Areas Commun 15: 614–625

    Article  Google Scholar 

  15. Orsak GC, Aazhang B (1991) Constrained solutions in importance sampling via robust statistics. IEEE Trans Inf Theory 37: 307–316

    Article  MATH  MathSciNet  Google Scholar 

  16. Sanz-González JL, Andina D (1999) Performance analysis of neural network detectors by importance sampling techniques. Neural Process Lett 9: 257–269

    Article  Google Scholar 

  17. Gerlach K (1999) New results in importance sampling. IEEE Trans Aerosp Electron Syst 35: 917–925

    Article  Google Scholar 

  18. Orsak GC (1993) A note on estimating false alarm rates via importance sampling. IEEE Trans Commun 41: 1275–1277

    Article  MATH  Google Scholar 

  19. Hoogerheide LF, Kaashoek JF, van Dijk HK (2007) On the shape of posterior densities and credible sets in instrumental variable regression models with reduced rank: an application of flexible sampling methods using neural networks. J Econom 139: 154–180

    Article  Google Scholar 

  20. Hoogerheide LF, van Dijk HK (2010) Bayesian forecasting of value at risk and expected shortfall using adaptive importance sampling. Int J Forecast 26(2): 231–247

    Article  Google Scholar 

  21. Gandhi PP, Ramamurti V (1997) Neural networks for signal detection in non-Gaussian noise. IEEE Trans Signal Process 45: 2846–2851

    Article  Google Scholar 

  22. Andina D, Sanz-González JL (1996) Comparison of a neural network detector vs. Neyman–Pearson optimal detector. In: Proceedings of the IEEE international conference on acoustics, speech, and signal processing (ICASSP’96), May 7–10, vol 6, pp 3573–3576

  23. Jarabo-Amores MP, Rosa-Zurera M, Gil-Pita R, López-Ferreras F (2009) Study of two error functions to approximate the Neyman–Pearson detector using supervised learning machines. IEEE Trans Signal Process 57: 4175–4181

    Article  Google Scholar 

  24. Sanz-González JL, Andina D (2001) Importance sampling techniques in neural detector training. Lect Notes Comput Sci 2167: 431–436

    Article  Google Scholar 

  25. Sanz-González JL, Andina D, Seijas J (2002) Importance sampling and mean-square error in neural detector training. Neural Process Lett 16: 259–276

    Article  MATH  Google Scholar 

  26. Rosa-Zurera M, Jarabo-Amores P, López-Ferreras F, Sanz-González JL (2005) Comparative analysis of importance sampling techniques to estimate error functions for training neural networks. In: Proceedings of the IEEE 13th workshop on statistical signal processing, July 17–20, pp 121–125

  27. Hachiya H, Akiyama T, Sugiayma S, Peters J (2009) Adaptive importance sampling for value function approximation in off-policy reinforcement learning. Neural Netw 22: 1399–1410

    Article  Google Scholar 

  28. Poor HV (1994) An introduction to signal detection and estimation, 2nd edn. Springer, Berlin

    MATH  Google Scholar 

  29. Hampshire JB, Pearlmutter B (1990) Equivalence proofs for multilayer perceptron classifiers and the Bayesian discriminant function. In: Proceedings of the 1990 Connectionist Models Summer School, pp 159–172

  30. Van Trees HL (2003) Detection, estimation and modulation theory. Part I. Wiley, New York

    Google Scholar 

  31. Haykin S (2008) Neural networks and learning machines, 3rd edn. Prentice-Hall, London

    Google Scholar 

  32. Seiffer U (2001) Multiple layer perceptron training using genetic algorithms. In: Proceedings of the 2001 European symposium on artificial neural networks, pp 159–164

  33. Montana DJ, Davis L (1989) Training feedforward neural networks using genetic algorithms. In: Proceedings of 11th international joing conference on artificial intelligence, pp 762–767

  34. Nguyen D, Widrow B (1990) Improving the learning speed of 2-layer neural networks by choosing initial values of the adaptive weights. In: Proceedings of the 1990 international joint conference on neural networks (IJCN 1990), June 17–21, vol 3, pp 21–26

Download references

Author information

Authors and Affiliations

  1. Signal Theory and Communications Department, Superior Polytechnic School, University of Alcalá, Ctra. Madrid-Barcelona, km. 33.1, 28805, Alcalá de Henares, Madrid, Spain

    Raúl Vicen-Bueno, M. Pilar Jarabo-Amores, Manuel Rosa-Zurera & Saturnino Maldonado-Bascón

  2. Signals, Systems and Radiocommunications Department, ETSI de Telecomunicación, Polytechnic University of Madrid, Ciudad Universitaria, 28040, Madrid, Spain

    José L. Sanz-González

Authors
  1. Raúl Vicen-Bueno
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Pilar Jarabo-Amores
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Manuel Rosa-Zurera
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. José L. Sanz-González
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Saturnino Maldonado-Bascón
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Manuel Rosa-Zurera.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Vicen-Bueno, R., Jarabo-Amores, M.P., Rosa-Zurera, M. et al. Importance Sampling for Objective Function Estimations in Neural Detector Training Driven by Genetic Algorithms. Neural Process Lett 32, 249–268 (2010). https://doi.org/10.1007/s11063-010-9155-8

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11063-010-9155-8

Keywords

Search

Navigation