Cost functions to estimate a posteriori probabilities in multiclass problems

  • Authors:
  • J. Cid-Sueiro;J. I. Arribas;S. Urban-Munoz;A. R. Figueiras-Vidal

  • Affiliations:
  • Dept. de Teoria de la Senal y Comunicaciones e Ing. Telematica, Univ. de Valiadolid;-;-;-

  • Venue:
  • IEEE Transactions on Neural Networks
  • Year:
  • 1999

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Abstract

The problem of designing cost functions to estimate a posteriori probabilities in multiclass problems is addressed. We establish necessary and sufficient conditions that these costs must satisfy in one-class one-output networks whose outputs are consistent with probability laws. We focus our attention on a particular subset of the corresponding cost functions which verify two common properties: symmetry and separability (well-known cost functions, such as the quadratic cost or the cross entropy are particular cases in this subset). Finally, we present a universal stochastic gradient learning rule for single-layer networks, in the sense of minimizing a general version of these cost functions for a wide family of nonlinear activation functions