Abstract
A new stochastic procedure is applied to optimization problems that arise in the nonlinear modeling of data. The proposed technique is an implementation of a recently introduced algorithm for the construction of probability densities that are consistent with the asymptotic statistical properties of general stochastic search processes. The obtained densities can be used, for instance, to draw suitable starting points in nonlinear optimization algorithms. The proposed setup is tested on a benchmark global optimization example and in the weight optimization of an artificial neural network model. Two additional examples that illustrate aspects that are specific to data modeling are outlined.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Berrones, A.: Generating Random Deviates Consistent with the Long Term Behavior of Stochastic Search Processes in Global Optimization. LNCS, vol. 4507, pp. 1–8. Springer, Heidelberg (2007)
Geman, S., Geman, D.: Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Trans. Pattern Anal. Mach. Intell. 6, 721–741 (1984)
Grasman, J., van Herwaarden, O.A.: Asymptotic Methods for the Fokker–Planck Equation and the Exit Problem in Applications. Springer, Heidelberg (1999)
Haykin, S.: Neural Networks: a Comprehensive Foundation. Prentice Hall, New Jersey (1999)
Kantz, H., Schreiber, T.: Nonlinear Time Series Analysis. Cambridge University Press, Cambridge (2004)
Kirkpatrick, S., Gelatt Jr., C.D., Vecchi, M.P.: Optimization by Simulated Annealing. Science 220, 671–680 (1983)
Ott, E.: Chaos in Dynamical Systems. Cambridge University Press, Cambridge (1993)
Pardalos, P.M., Schoen, F.: Recent Advances and Trends in Global Optimization: Deterministic and Stochastic Methods. In: DSI 1–2004. Proceedings of the Sixth International Conference on Foundations of Computer–Aided Process Design, pp. 119–131 (2004)
Parsopoulos, K.E., Vrahatis, M.N.: Recent approaches to global optimization problems through Particle Swarm Optimization. Natural Computing 1, 235–306 (2002)
Pavlidis, N.G., Plagianakos, V.P., Tasoulis, D.K., Vrahatis, D.K.: Human Designed Vs. Genetically Programmed Differetial Evolution Operators IEEE Congress on Evolutionary Computation, pp. 1880–1886. IEEE Computer Society Press, Los Alamitos (2006)
Press, W., Teukolsky, S., Vetterling, W., Flannery, B.: Numerical Recipes in C++, the Art of Scientific Computing. Cambridge University Press, Cambridge (2005)
Risken, H.: The Fokker–Planck Equation. Springer, Heidelberg (1984)
Schweitzer, F.: Brownian Agents and Active Particles: Collective Dynamics in the Natural and Social Sciences. Springer, Berlin (2003)
Suykens, J.A.K., Vandewalle, J.: Artificial Neural Networks for Modelling and Control of Non-Linear Systems. Springer, Berlin (1996)
Suykens, J.A.K., Verrelst, H., Vandewalle, J.: On–Line Learning Fokker–Planck Machine. Neural Processing Letters 7(2), 81–89 (1998)
Van Kampen, N.G.: Stochastic Processes in Physics and Chemistry. North-Holland, Amsterdam (1992)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Peña, D., Sánchez, R., Berrones, A. (2007). Stationary Fokker – Planck Learning for the Optimization of Parameters in Nonlinear Models. In: Gelbukh, A., Kuri Morales, Á.F. (eds) MICAI 2007: Advances in Artificial Intelligence. MICAI 2007. Lecture Notes in Computer Science(), vol 4827. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-76631-5_10
Download citation
DOI: https://doi.org/10.1007/978-3-540-76631-5_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-76630-8
Online ISBN: 978-3-540-76631-5
eBook Packages: Computer ScienceComputer Science (R0)