Abstract
The theoretical framework of Statistical Learning Theory (SLT) for pattern recognition problems is extended to comprehend the situations where an infinite value of the loss function is employed to prevent misclassifications in specific regions with high reliability.
Sufficient conditions for ensuring the consistency of the Empirical Risk Minimization (ERM) criterion are then established and an explicit bound, in terms of the VC dimension of the class of decision functions employed to solve the problem, is derived.
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References
Vapnik, V. N. (1982). Estimation of Dependences Based on Empirical Data. New York: Springer-Verlag.
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Vapnik, V. N. and Chervonenkis, A. Ya. (1971). On the uniform convergence of relative frequencies of events to their probabilities. Theory of Probability and Its Applications, pages 264–280.
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Muselli, M., Ruffino, F. (2005). Consistency of Empirical Risk Minimization for Unbounded Loss Functions. In: Apolloni, B., Marinaro, M., Tagliaferri, R. (eds) Biological and Artificial Intelligence Environments. Springer, Dordrecht. https://doi.org/10.1007/1-4020-3432-6_31
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DOI: https://doi.org/10.1007/1-4020-3432-6_31
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-3431-2
Online ISBN: 978-1-4020-3432-9
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