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Rigorous Learning Curve Bounds from Statistical Mechanics (1996)  (Make Corrections)  (47 citations)
David Haussler, Michael Kearns, H. Sebastian Seung, Naftali Tishby
Computational Learing Theory



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Abstract: . In this paper we introduce and investigate a mathematically rigorous theory of learning curves that is based on ideas from statistical mechanics. The advantage of our theory over the well-established VapnikChervonenkis theory is that our bounds can be considerably tighter in many cases, and are also more reflective of the true behavior of learning curves. This behavior can often exhibit dramatic properties such as phase transitions, as well as power law asymptotics not explained by the VC... (Update)

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BibTeX entry:   (Update)

Haussler, D., Kearns, M., Seung, H., and Tishby, N. (1996). Rigorous learning curve bounds from statistical mechanics. MACHINE LEARNING, 25:195--236. http://citeseer.ist.psu.edu/haussler96rigorous.html   More

@inproceedings{ haussler94rigorous,
    author = "David Haussler and H. Sebastian Seung and Michael J. Kearns and Naftali Tishby",
    title = "Rigorous Learning Curve Bounds from Statistical Mechanics",
    booktitle = "Computational Learing Theory",
    pages = "76-87",
    year = "1994",
    url = "citeseer.ist.psu.edu/haussler96rigorous.html" }
Citations (may not include all citations):
2319   Elements of Information Theory (context) - Cover, Thomas - 1991  ACM
454   the uniform convergence of relative frequencies of events to.. (context) - Vapnik, Chervonenkis - 1971
348   Estimation of Dependences Based on Empirical Data (context) - Vapnik - 1982
318   Convergence of Stochastic Processes (context) - Pollard - 1984
268   Decision-theoretic generalizations of the PAC model for neur.. (context) - Haussler - 1992
151   A general lower bound on the number of examples needed for l.. (context) - Ehrenfeucht, Haussler et al. - 1989
59   Central limit theorems for empirical measures (context) - Dudley - 1978
58   Statistical mechanics of learning from examples (context) - Seung, Sompolinsky et al. - 1992
44   A statistical approach to learning and generalization in neu.. (context) - Levin, Tishby et al. - 1989
40   The statistical mechanics of learning a rule (context) - Watkin, Rau et al. - 1993
37   The space of interactions in neural network models (context) - Gardner - 1988
29   Measuring the VC dimension of a learning machine - --, Levin et al. - 1994
25   Recognizing hand-printed letters and digits using backpropag.. (context) - Martin, Pittman - 1991  ACM
24   Learnability with respect to fixed distributions (context) - Benedek, Itai - 1991  ACM   DBLP
24   Statistical theory of learning a rule (context) - --, Tishby - 1990
20   Four types of learning curves - Amari, Fujita et al. - 1992  ACM
13   How tight are the Vapnik-Chervonenkis bounds (context) - Cohn, Tesauro - 1992
13   General bounds on the number of examples needed for learning.. (context) - Simon - 1993
12   Lower bounds in pattern recognition and learning (context) - Devroye, Lugosi - 1994
11   The transition to perfect generalization in perceptrons (context) - Baum, Lyuu - 1991  ACM
11   the sample complexity of weak learning (context) - Goldman, Kearns et al. - 1990
10   Learning curves in large neural networks (context) - Sompolinsky, Seung et al. - 1991  ACM   DBLP
8   Implementing Valiant's learnability theory using random sets (context) - Comput, Oblow - 1992  ACM   DBLP
8   First-order transition to perfect generalization in a neural.. (context) - Gyorgyi - 1990
7   Average case analysis of empirical and explanation-based lea.. (context) - Sarrett, Pazzani - 1992
5   Systems that can learn from examples: replica calculation of.. (context) - Phys, Engel et al. - 1993
5   Learning Theory (context) - Comput - 1990  ACM
4   Statistical mechanics calculation of Vapnik Chervonenkis bou.. (context) - Engel, Fink - 1993
4   Three unfinished works on the optimal storage capacity of ne.. (context) - Gardner, Derrida - 1989
1   Exhaustive learning (context) - Learning, Schwartz et al. - 1990
1   Workshop on Comput (context) - Rivest, Proc et al. - 1992
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