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Title: | Learning by examples from a nonuniform distribution | Authors: | REIMANN, Peter VAN DEN BROECK, Christian |
Issue Date: | 1996 | Publisher: | AMERICAN PHYSICAL SOC | Source: | PHYSICAL REVIEW E, 53(4). p. 3989-3998 | Abstract: | 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 alpha(c) = 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. | Notes: | LIMBURGS UNIV CENTRUM,B-3590 DIEPENBEEK,BELGIUM. | Document URI: | http://hdl.handle.net/1942/3500 | DOI: | 10.1103/PhysRevE.53.3989 | ISI #: | A1996UH48200042 | Type: | Journal Contribution |
Appears in Collections: | Research publications |
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