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Title
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Learning by examples from a non-uniform distribution
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Author
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Abstract
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| We present a general replica calculation for learning from examples generated by a nonuniform pattern distribution with a single symmetry-breaking orientation. Our results cover the three main learning scenarios: storage of patterns with random classifications by a perceptron, supervised learning from a teacher, and unsupervised learning. We show that for a perceptron the critical storage capacity αc=2 is completely independent of the pattern distribution provided it is point symmetric or provided the classification as ± 1 is unbiased. In a particular model for supervised learning we find that an ideal (Bayes) student learns most from a few examples if they are easy and from a large number if they are difficult. Learning based on the minimization of a specific class of (quadratic) cost functions is solved completely for all three scenarios. |
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Language
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English
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Source (journal)
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Physical review : E : statistical, nonlinear, and soft matter physics / American Physical Society. - Melville, N.Y., 2001 - 2015
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Publication
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Melville, N.Y.
:
American Physical Society
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1996
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ISSN
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1539-3755
[print]
1550-2376
[online]
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Volume/pages
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53
(1996)
, p. 3989-3998
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ISI
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A1996UH48200042
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Full text (Publisher's DOI)
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Full text (open access)
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