Abstract
Here we present a novel probability density estimation model. The classical Parzen window approach builds a spherical Gaussian density around every input sample. Our proposal selects a Gaussian specifically tuned for each sample, with an automated estimation of the local intrinsic dimensionality of the embedded manifold and the local noise variance. This leads to outperform other proposals where local parameter selection is not allowed, like the manifold Parzen windows.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bishop, C.: Neural Networks for Pattern Recognition. Oxford University Press, Oxford (1995)
Silverman, B.: Density Estimation for Statistics and Data Analysis. Chapman and Hall, New York (1986)
Vapnik, V.N.: Statistical Learning Theory. John Wiley & Sons, New York (1998)
Izenman, A.J.: Recent developments in nonparametric density estimation. Journal of the American Statistical Association 86(413), 205–224 (1991)
Lejeune, M., Sarda, P.: Smooth estimators of distribution and density functions. Computational Statistics & Data Analysis 14, 457–471 (1992)
Hjort, N.L., Jones, M.C.: Locally Parametric Nonparametric Density Estimation. Annals of Statistics 24(4), 1619–1647 (1996)
Hastie, T., Loader, C.: Local regression: Automatic kernel carpentry. Statistical Science 8, 120–143 (1993)
McLachlan, G., Peel, D.: Finite Mixture Models. Wiley, Chichester (2000)
Parzen, E.: On the Estimation of a Probability Density Function and Mode. Annals of Mathematical Statistics 33, 1065–1076 (1962)
Vincent, P., Bengio, Y.: Manifold Parzen Windows. Advances in Neural Information Processing Systems 15, 825–832 (2003)
López-Rubio, E., Ortiz-de-Lazcano-Lobato, J.M., Vargas-González, M.C., López-Rubio, J.M.: Dynamic Selection of Model Parameters in Principal Components Analysis Neural Networks. In: Proceedings of the 16th European Conference on Artificial Intelligence (ECAI 2004), pp. 618–622 (2004)
López-Rubio, E., Ortiz-de-Lazcano-Lobato, J.M., Vargas-González, M.C.: Competitive Networks of Probabilistic Principal Components Analysis Neurons. In: 9th IASTED International Conference on Artificial Intelligence and Soft Computing (ASC 2005), pp. 141–146 (2005)
VizieR service (March 29, 2004), Online, Available at, http://vizier.cfa.harvard.edu/viz-bin/VizieR/
Chen, H.-W., et al.: Early-type galaxy progenitors beyond z=1. Astrophysical Journal 560, L131 (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
López-Rubio, E., Ortiz-de-Lazcano-Lobato, J.M., López-Rodríguez, D., Mérida-Casermeiro, E., del Carmen Vargas-González, M. (2006). Local Selection of Model Parameters in Probability Density Function Estimation. In: Kollias, S., Stafylopatis, A., Duch, W., Oja, E. (eds) Artificial Neural Networks – ICANN 2006. ICANN 2006. Lecture Notes in Computer Science, vol 4132. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11840930_30
Download citation
DOI: https://doi.org/10.1007/11840930_30
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-38871-5
Online ISBN: 978-3-540-38873-9
eBook Packages: Computer ScienceComputer Science (R0)