Estimating a boolean perceptron from its average satisfying assignment: A bound on the precision required
UNSPECIFIED (2001) Estimating a boolean perceptron from its average satisfying assignment: A bound on the precision required. In: 14th Annual Conference on Computational Learning Theory (COLT 2001)/5th European Conference on Computational Learning Theory (EuroCOLT 2001), AMSTERDAM, NETHERLANDS, JUL 16-19, 2001. Published in: COMPUTATIONAL LEARNING THEORY, PROCEEDINGS, 2111 pp. 116-127.Full text not available from this repository.
A boolean perceptron is a linear threshold function over the discrete boolean domain (0, 1)(n). That is, it maps any binary vector to 0 or I depending on whether the vector's components satisfy some linear inequality. In 1961, Chow  showed that any boolean perceptron is determined by the average or "center of gravity" of its "true" vectors (those that are mapped to 1). Moreover, this average distinguishes the function from any other boolean function, not just other boolean perceptrons. We address an associated statistical question of whether an empirical estimate of this average is likely to provide a good approximation to the perceptron. In this paper we show that an estimate that is accurate to within additive error (epsilon/n)(O(log(1/epsilon))) determines a boolean perceptron that is accurate to within error e (the fraction of misclassified vectors). This provides a mildly super-polynomial bound on the sample complexity of learning boolean perceptrons in the "restricted focus of attention" setting. In the process we also find some interesting geometrical properties of the vertices of the unit hypercube.
|Item Type:||Conference Item (UNSPECIFIED)|
|Subjects:||Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software|
|Series Name:||LECTURE NOTES IN ARTIFICIAL INTELLIGENCE|
|Journal or Publication Title:||COMPUTATIONAL LEARNING THEORY, PROCEEDINGS|
|Editor:||Helmbold, D and Williamson, B|
|Number of Pages:||12|
|Page Range:||pp. 116-127|
|Title of Event:||14th Annual Conference on Computational Learning Theory (COLT 2001)/5th European Conference on Computational Learning Theory (EuroCOLT 2001)|
|Location of Event:||AMSTERDAM, NETHERLANDS|
|Date(s) of Event:||JUL 16-19, 2001|
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