The DOI matches its Crossref record; 32 of the 32 references it cites were found in a registry or an index.
What Size Net Gives Valid Generalization?
Abstract
We address the question of when a network can be expected to generalize from m random training examples chosen from some arbitrary probability distribution, assuming that future test examples are drawn from the same distribution. Among our results are the following bounds on appropriate sample vs. network size. Assume 0 < ∊ ≤ 1/8. We show that if m ≥ O(W/∊ log N/∊) random examples can be loaded on a feedforward network of linear threshold functions with N nodes and W weights, so that at least a fraction 1 − ∊/2 of the examples are correctly classified, then one has confidence approaching certainty that the network will correctly classify a fraction 1 − ∊ of future test examples drawn from the same distribution. Conversely, for fully-connected feedforward nets with one hidden layer, any learning algorithm using fewer than Ω(W/∊) random training examples will, for some distributions of examples consistent with an appropriate weight choice, fail at least some fixed fraction of the time to find a weight choice that will correctly classify more than a 1 − ∊ fraction of the future test examples.
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Cites
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Backpropagation Applied to Handwritten Zip Code Recognition
LeCun, Y., Boser, B., Denker, J. S., Henderson, D., Howard, R. E., Hubbard, W., & Jackel, L. D. (1989) · Neural Computation · doi:10.1162/neco.1989.1.4.541 · Cited by 11,891
On the Uniform Convergence of Relative Frequencies of Events to Their Probabilities
Vapnik, V. N., & Chervonenkis, A. Y. (2015) · Measures of Complexity · doi:10.1007/978-3-319-21852-6_3 · Cited by 3,105
Estimation of Dependences Based on Empirical Data
Vapnik, V. (2006) · Information Science and Statistics · doi:10.1007/0-387-34239-7 · Cited by 2,238
Convergence of Stochastic Processes.
Robinson, P. M., & Pollard, D. (1985) · Economica · doi:10.2307/2553898 · Cited by 2,184
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Learnability and the Vapnik-Chervonenkis dimension
Blumer, A., Ehrenfeucht, A., Haussler, D., & Warmuth, M. K. (1989) · Journal of the ACM · doi:10.1145/76359.76371 · Cited by 1,839
Self-citationParallel Networks that Learn to Pronounce English Text
B, T. J. S. A. (1987) · Cited by 1,514
Connectionist learning procedures
Hinton, G. E. (1989) · Artificial Intelligence · doi:10.1016/0004-3702(89)90049-0 · Cited by 1,430
Learning Quickly When Irrelevant Attributes Abound: A New Linear-Threshold Algorithm
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Cited by
A decision-theoretic generalization of on-line learning and an application to boosting
Freund, Y., & Schapire, R. E. (1997) · Journal of Computer and System Sciences · doi:10.1006/jcss.1997.1504 · Cited by 20,466
Deep learning in neural networks: an overview
Schmidhuber, J. (2015) · Neural Networks · doi:10.1016/j.neunet.2014.09.003 · Cited by 18,570
Approximation by superpositions of a sigmoidal function
Cybenko, G. (1989) · Mathematics of Control, Signals, and Systems · doi:10.1007/bf02551274 · Cited by 13,883
A training algorithm for optimal margin classifiers
Boser, B. E., Guyon, I. M., & Vapnik, V. N. (1992) · Proceedings of the fifth annual workshop on Computational learning theory · doi:10.1145/130385.130401 · Cited by 11,992
Backpropagation Applied to Handwritten Zip Code Recognition
LeCun, Y., Boser, B., Denker, J. S., Henderson, D., Howard, R. E., Hubbard, W., & Jackel, L. D. (1989) · Neural Computation · doi:10.1162/neco.1989.1.4.541 · Cited by 11,891
Metadata
- Authors
- Baum, E. B., & Haussler, D.
- Venue
- Neural Computation
- Publisher
- MIT Press - Journals
- Published
- 1989-03
- Volume
- 1
- Issue
- 1
- Pages
- 151-160
- ISSN
- 0899-7667 (ISSN-L)
- 1530-888X
- OpenAlex
- W2165758113
- Cited by
- 1,541
- References
- 32
- FWCI
- 62.41
- Type
- journal article
- Language
- en
- Open access
- closed
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
