Abstract
Given a class F of densities, we are to construct a density estimate such that it performs almost as well as the best density in the class. We saw that the skeleton estimate defined in the previous chapter always works when F is totally bounded. In this chapter we analyze the minimum distance estimate described in Section 6.8. Assume that the densities f θ ∈ F are indexed by a parameter θ ∈ Θ.
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§8.8. References
M. Anthony and P. L. Bartlett, Neural Network Learning: Theoretical Foundations, Cambridge University Press, Cambridge, 1999.
P. L. Butzer and R. J. Nessel, Fourier Analysis and Approximation, Birkhäuser-Verlag, Basel, 1971.
L. Devroye and L. Györfl, Nonparametric Density Estimation: The L1 View, Wiley, New York, 1985.
L. Devroye, L. Györfl, and G. Lugosi, A Probabilistic Theory of Pattern Recognition, Springer-Verlag, New York, 1996.
P. Goldberg and M. Jerrum, “Bounding the Vapnik-Chervonenkis dimension of concept classes parametrized by real numbers,” Machine Learning, vol. 18, pp. 131–148, 1995.
M. Karpinski and A. Macintyre, “Polynomial bounds for VC dimension of sigmoidal and general pfaffian neural networks,” Journal of Computer and System Science, vol. 54, pp. 169–176, 1997.
A. G. Khovanskii, “Fewnomials,” in: Translations of Mathematical Monographs, vol. 88, American Mathematical Society, Providence, RI, 1991.
P. Koiran and E. D. Sontag, “Neural networks with quadratic VC dimension,” Journal of Computer and System Science, vol. 54, pp. 190–198, 1997.
A. Krzyżak and T. Linder, “Radial basis function networks and complexity regularization in function learning,” IEEE Transactions on Neural Networks, vol. 9, pp. 247–256, 1998.
A. Macintyre and E. D. Sontag, “Finiteness results for sigmoidal neural networks,” in: Proceedings of the 25th Annual ACM Symposium on the Theory of Computing, pp. 325–334, Association of Computing Machinery, New York, 1993.
T. Poggio and F. Girosi, “A theory of networks for approximation and learning,” Proceedings of the IEEE, vol. 78, pp. 1481–1497, 1990.
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Devroye, L., Lugosi, G. (2001). The Minimum Distance Estimate: Examples. In: Combinatorial Methods in Density Estimation. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-0125-7_8
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DOI: https://doi.org/10.1007/978-1-4613-0125-7_8
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