# Cost functions to estimate a posteriori probabilities in multiclass problems

Title | Cost functions to estimate a posteriori probabilities in multiclass problems |

Publication Type | Journal Article |

Year of Publication | 1999 |

Authors | Cid-Sueiro, J., J. I. Arribas, S. Urban-Munoz, and A. R. Figueiras-Vidal |

Journal | IEEE Transactions on Neural Networks |

Volume | 10 |

Pagination | 645-656 |

ISSN | 10459227 |

Keywords | Cost functions, Estimation, Functions, Learning algorithms, Multiclass problems, Neural networks, Pattern recognition, Probability, Problem solving, Random processes, Stochastic gradient learning rule |

Abstract | The problem of designing cost functions to estimate a posteriori probabilities in multiclass problems is addressed in this paper. 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; those which verify two usually interesting 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. |

URL | http://www.scopus.com/inward/record.url?eid=2-s2.0-0032643080&partnerID=40&md5=d528195bd6ec84531e59ddd2ececcd46 |

DOI | 10.1109/72.761724 |