Cost functions to estimate a posteriori probabilities in multiclass problems.
Identifieur interne : 000405 ( PubMed/Curation ); précédent : 000404; suivant : 000406Cost functions to estimate a posteriori probabilities in multiclass problems.
Auteurs : J. Cid-Sueiro [Espagne] ; J I Arribas ; S. Urbán-Mu Oz ; A R Figueiras-VidalSource :
- IEEE transactions on neural networks / a publication of the IEEE Neural Networks Council [ 1045-9227 ] ; 1999.
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.
DOI: 10.1109/72.761724
PubMed: 18252565
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