Continuous Risk Functionals

  • Joaquim P. Marques de Sá
  • Luís M. A. Silva
  • Jorge M. F. Santos
  • Luís A. Alexandre
Part of the Studies in Computational Intelligence book series (SCI, volume 420)

Abstract

As explained in the preceding chapter, the learning algorithm needed to adequately tune a regression-like classifier, based on the information provided by a training set, consists of the minimization of a quantity called risk, whose expression is given by formula (1.7). This formula assigns a number, R L (Y w ), to a function y w , i.e., the formula is an instantiation of an Y W = y w → ℝ mapping. Such mapping type (from a set of functions onto a set of numbers) is called a functional. The risk functional, expressed in terms of a continuous and differentiable loss function L(t(x), y w (x)), is minimized by some algorithm attempting to find a classifier with a probability of error hopefully close to that of z w*: min P e .

Keywords

Loss Function Shannon Entropy Empirical Risk Quadratic Entropy Risk Functional 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Berlin Heidelberg 2013

Authors and Affiliations

  • Joaquim P. Marques de Sá
    • 1
  • Luís M. A. Silva
    • 2
  • Jorge M. F. Santos
    • 3
  • Luís A. Alexandre
    • 4
  1. 1.Divisão de Sinal e Imagem Campus FEUPINEB-Instituto de Engenharia BiomédicaPortoPortugal
  2. 2.Dept. of MathematicsUniv. de AveiroAveiroPortugal
  3. 3.Dept. of MathematicsISEP, School of Engineering Polytechnic of PortoPortoPortugal
  4. 4.Dept. of InformaticsUniv. Beira Interior IT - Instituto de TelecomunicaçõesCovilhãPortugal

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