Abstract
A lot of learning machines which have the hidden variables or the hierarchical structures are the singular statistical models. They have a different learning performance from the regular statistical models. In this paper, we show that the learning coefficient is easily computed by weighted blow up, in contrast, and that there is the case that the learning coefficient cannot be correctly computed by blowing up at the origin O only.
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References
Arnol’d, I.V.: Normal forms of functions in neighbourhoods of degenerate critical points. Russian Mathematical Surveys 29(2), 10–50 (1974)
Aoyagi, M., Watanabe, S.: Stochastic complexities of reduced rank regression in Bayesian estimation. Neural Networks 18(7), 924–933 (2005)
Aoyagi, M., Watanabe, S.: Resolution of singularities and generalization error with Bayesian estimation for layered neural network. IEICE Trans. J88-D-II(10), 2112–2124 (2005)
Atiyah, M.: Resolution of singularities and division of distributions. Communications of Pure and Applied Mathematics 13, 145–150 (1970)
Fulton, W.: Introduction to Toric Varieties, vol. 131. Princeton University Press, Princeton (1993)
Matsuda, T., Watanabe, S.: Analytic Equivalence of Bayes a Posteriori Distributions. In: Kollias, S., Stafylopatis, A., Duch, W., Oja, E. (eds.) ICANN 2006. LNCS, vol. 4131, pp. 113–121. Springer, Heidelberg (2006)
Watanabe, S.: Algebraic Analysis for Non-identifiable Learning Machines. Neural Computation 13(4), 899–933 (2001)
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Matsuda, T., Watanabe, S. (2007). On a Singular Point to Contribute to a Learning Coefficient and Weighted Resolution of Singularities. In: de Sá, J.M., Alexandre, L.A., Duch, W., Mandic, D. (eds) Artificial Neural Networks – ICANN 2007. ICANN 2007. Lecture Notes in Computer Science, vol 4668. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74690-4_2
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DOI: https://doi.org/10.1007/978-3-540-74690-4_2
Publisher Name: Springer, Berlin, Heidelberg
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