On-line Learning of Perceptron from Noisy Data by One and Two Teachers(General)

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概要

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• We analyze the on-line learning of a Perceptron from signals produced by a single Perceptron suffering from external noise or by two independent Perceptrons without noise. We adopt typical three learning rules in both single-teacher and two-teacher cases. For the single-teacher case, we treat the input and output noises and for the two-teacher case, we assume that signals are given by two teachers with a definite probability. In the single-teacher case, in order to improve the learning when it does not succeed in the sense that the student vector does not converge to the teacher vector, we use two methods: a method based on the optimal learning rate and an averaging method. Furthermore, we obtain an asymptotic form of the generalization error using an optimal learning rate for the three learning rales, and we estimate noise parameters using the simulation data by the averaging method. In the two-teacher case, for the Hebbian rule, we give analytical solutions of order parameters. Furthermore, we estimate noise parameters using the Perceptron rule by the averaging method. The theoretical results agree quite well with the numerical simulations.

• 社団法人日本物理学会の論文
• 2006-11-15

著者

• Maeda Yoshiko

  Graduate School Of Sciences And Humanities Nara Women's University:(present Address)mitsubishi

• UEZU Tatsuya

  Graduate School of Humanities and Sciences, Nara Women's University

• Uezu Tatsuya

  Graduate School Of Sciences And Humanities Nara Women's University

• Uezu Tatsuya

  Graduate School Of Human Culture Nara Women's University

• YAMAGUCHI Sachi

  Faculty of Sciences, Department of Physics, Nara Women's University

• Yamaguchi Sachi

  Faculty Of Sciences Department Of Physics Nara Women's University:(present Address)graduate Sch

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