Abstract
We describe an efficient method for accurate estimation of the score function of a random variable, which can be regarded as an extension of the FFT-based fast density estimation method of Silverman (1982), and which scales no more than linearly with the sample size. We demonstrate the utility of our approach in a real-life ICA problem involving the separation of eight sound signals, where better results are observed than using state-of-the-art ICA methods.
This research is supported by the Dutch Technology Foundation STW, applied science division of NWO, and the technology programme of the Ministry of Economic Affairs, project AIF 4997.
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
S. Amari and J.-F. Cardoso. Blind source Separation-semiparametric statistical approach. IEEE Trans. Signal Processing, 45(11):2692–2700, 1997.
S. Amari, A. Cichocki, and H. H. Yang. A new learning algorithm for blind signal Separation. In D. S. Touretzky, M. C. Mozer, and M. E. Hasselmo, editors, Advances in Neural Information Processing Systems, volume 8, pages 757–763. The MIT Press, 1996.
H. Attias. Independent factor analysis. Neural Computation, 11:803–851, 1999.
A. J. Bell and T. J. Sejnowski. An information-maximization approach to blind separation and blind deconvolution. Neural Computation, 7:1129–1159, 1995.
J.-F. Cardoso. Blind signal Separation: statistical principles. Proc. IEEE, 9(10):2009–2025, Oct. 1998.
P. Hall. On projection pursuit regression. Ann. Statist., 17(2):573–588, 1989.
T.-W. Lee, M. Girolami, and T. Sejnowski. Independent component analysis using an extended infomax algorithm for mixed sub-Gaussian and super-Gaussian sources. Neural Computation, 11(2):409–433, 1999.
G. J. McLachlan and D. Peel. Finite Mixture Models. Wiley, New York, 2000.
E. Moulines, J.-F. Cardoso, and E. Gassiat. Maximum likelihood for blind separation and deconvolution of noisy signals using mixture models. In Proc. ICASSP, pages 3617–3620, Munich, Germany, 1997.
B. A. Pearlmutter and L. C. Parra. A context-sensitive generalization of ICA. In Proc. Int. Conf. on Neural Information Processing, Hong Kong, 1996.
W. H. Press, S. A. Teukolsky, B. P. Flannery, and W. T. Vetterling. Numerical Recipes in C. Cambridge University Press, 2nd edition, 1992.
B. W. Silverman. Kernel density estimation using the Fast Fourier Transform. Appl. Statist., 31:93–99, 1982.
N. Vlassis and Y. Motomura. Efficient source adaptivity in independent component analysis. IEEE Trans. Neural Networks, 12(3), May 2001.
M. P. Wand and M. C. Jones. Kernel Smoothing. Chapman & Hall, London, 1995.
L. Xu, C. C. Cheung, and S. Amari. Learned parametric mixture based ICA algorithm. Neurocomputing, 22:69–80, 1998.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Vlassis, N. (2001). Fast Score Function Estimation with Application in ICA. In: Dorffner, G., Bischof, H., Hornik, K. (eds) Artificial Neural Networks — ICANN 2001. ICANN 2001. Lecture Notes in Computer Science, vol 2130. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44668-0_76
Download citation
DOI: https://doi.org/10.1007/3-540-44668-0_76
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42486-4
Online ISBN: 978-3-540-44668-2
eBook Packages: Springer Book Archive