Abstract
We consider a variant of the ‘population learning model’ proposed by Kearns and Seung, in which the learner is required to be ‘distribution-free’ as well as computationally efficient. A population learner receives as input hypotheses from a large population of agents and produces as output its final hypothesis. Each agent is assumed to independently obtain labeled sample for the target concept and outputs a hypothesis. A polynomial time population learner is said to ‘PAC learn’ a concept class, if its hypothesis is probably approximately correct whenever the population size exceeds a certain bound which is polynomial, even if the sample size for each agent is fixed at some constant. We exhibit some general population learning strategies, and some simple concept classes that can be learned by them. These strategies include the ‘supremum hypothesis finder,’ the ‘minimum superset finder’ (a special case of the ‘supremum hypothesis finder’), and various voting schemes. When coupled with appropriate agent algorithms, these strategies can learn a variety of simple concept classes, such as the ‘high-low game,’ conjunctions, axis-parallel rectangles and others. We give upper bounds on the required population size for each of these cases, and show that these systems can be used to obtain a speed up from the ordinary PAC-learning model, with appropriate choices of sample and population sizes. With the population learner restricted to be a voting scheme, what we have is effectively a model of ‘population prediction,’ in which the learner is to predict the value of the target concept at an arbitrarily drawn point, as a threshold function of the predictions made by its agents on the same point. We show that the population learning model is strictly more powerful than the population prediction model. Finally we consider a variant of this model with classification noise, and exhibit a population learner for the class of conjunctions in this model.
Real World Computing Partnership
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
D. Angluin and P. Laird. Learning from noisy examples. Machine Learning, 2:343–370, 1988.
W. Feller. An Introduction to Probability and its Applications, volume 2. John Wiley and Sons, second edition, 1971.
P. Fischer and H. U. Simon. On learning ring-sum-expansions. SIAM J. Comput., 21(1):181–192, 1992.
S. Goldman, M. Kearns, and R. Schapire. On the sample complexity of weak learning. In Proceedings of the 1990 Workshop on Computational Learning Theory. Morgan Kaufmann, San Mateo, California, August 1990.
D. Helmbold, R. Sloan, and M. K. Warmuth. Learning nested differences of intersection closed concept classes. Machine Learning, 5 (1), June 1990.
M. Kearns and S. Seung. Learning from a population of hypotheses. In Proceedings of the Sixth Annual ACM Workshop on Computational Learning Theory. Morgan Kaufmann, San Mateo, California, August 1993.
B. K. Natarajan. On learning boolean functions. In Proc. 19th ACM Symp. on Theory of Computing, pages 296–304, 1987.
L. G. Valiant. A theory of the learnable. Communications of A.C.M., 27:1134–1142, 1984.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1994 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Nakamura, A., Abe, N., Takeuchi, Ji. (1994). Efficient distribution-free population learning of simple concepts. In: Arikawa, S., Jantke, K.P. (eds) Algorithmic Learning Theory. AII ALT 1994 1994. Lecture Notes in Computer Science, vol 872. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58520-6_86
Download citation
DOI: https://doi.org/10.1007/3-540-58520-6_86
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-58520-6
Online ISBN: 978-3-540-49030-2
eBook Packages: Springer Book Archive