Abstract
A statistical theory for overtraining is proposed. The analysis treats general realizable stochastic neural networks, trained with Kullback-Leibler divergence in the asymptotic case of a large number of training examples. It is shown that the asymptotic gain in the generalization error is small if we perform early stopping, even if we have access to the optimal stopping time. Considering cross-validation stopping we answer the question: In what ratio the examples should be divided into training and cross-validation sets in order to obtain the optimum performance. Although cross-validated early stopping is useless in the asymptotic region, it surely decreases the generalization error in the nonasymptotic region. Our large scale simulations done on a CM5 are in nice agreement with our analytical findings.
Original language | English |
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Pages (from-to) | 985-996 |
Number of pages | 12 |
Journal | IEEE Transactions on Neural Networks |
Volume | 8 |
Issue number | 5 |
DOIs | |
Publication status | Published - 1997 |
Bibliographical note
Funding Information:Manuscript received September 11, 1995; revised October 21, 1996 and May 10, 1997. K.-R. Müller was supported in part by the EC S & T fellowship (FTJ 3-004). This work was supported by the National Institutes of Health (P41RRO 5969) and CNCPST Paris (96JR063).
Keywords
- Asymptotic analysis
- Cross-validation
- Early stopping
- Generalization
- Overtraining
- Stochastic neural networks
ASJC Scopus subject areas
- Software
- Computer Science Applications
- Computer Networks and Communications
- Artificial Intelligence