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Abstract: In this paper, we consider the problem of active learning in trigonometric polynomial networks and give a necessary and su#cient condition of sample points to provide the optimal generalization capability. By analyzing the condition from the functional analytic point of view, we clarify the mechanism of achieving the optimal generalization capability. We also show that a set of training examples satisfying the condition does not only provide the optimal generalization but also reduces the... (Update)
Context of citations to this paper: More
...on the optimality. One is the global optimal, where a set of all training examples is optimal (e.g. Fedorov [7] Sugiyama and Ogawa [21]) The other is the greedy optimal, where the next training example to sample is optimal in each step (e.g. MacKay [11] Cohn [3] 4]...
...the bias is explicitly evaluated by utilizing the knowledge of the distribution of the learning target functions. Vijayakumar et al. [24] extended the condition to the noisy case by dividing the sampling scheme into two stages. The first stage is for minimizing the bias...
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7: Neural network exploration using optimal experiment design - DA - 1994
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BibTeX entry: (Update)
Sugiyama, M., & Ogawa, H. (1999f). Training data selection for optimal generalization in trigonometric polynomial networks. to be published in S. A. Solla et al. (Eds.), Advances in Neural Information Processing Systems 12. http://citeseer.ist.psu.edu/sugiyama00training.html More
@misc{ sugiyama-training,
author = "M. Sugiyama and H. Ogawa",
title = "Training data selection for optimal generalization in trigonometric polynomial
networks",
text = "Sugiyama, M., & Ogawa, H. (1999f). Training data selection for optimal
generalization in trigonometric polynomial networks. to be published in
S. A. Solla et al. (Eds.), Advances in Neural Information Processing Systems
12.",
url = "citeseer.ist.psu.edu/sugiyama00training.html" }
Citations (may not include all citations):132 Theory of Optimal Experiments (context) - Fedorov - 1972
105 Information-based objective functions for active data select.. - MacKay - 1992
77 Neural network exploration using optimal experiment design - Cohn - 1994
43 Transactions on American Mathematical Society (context) - Aronszajn, reproducing - 1950
24 Active learning in multilayer perceptrons - Fukumizu - 1996
16 Projection filter regularization of ill-conditioned problem (context) - Ogawa - 1987
8 Theory of pseudo biorthogonal bases and its application (context) - Ogawa - 1998
6 generalization and over-learning (context) - Ogawa, learning - 1992
5 Functional analytic approach to model selection--- Subspace .. - Sugiyama, Ogawa - 1999
2 Incremental active learning in consideration of bias (context) - Sugiyama, Ogawa - 1999
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