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Cost functions to estimate a posteriori probabilities in multiclass problems

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4 Author(s)
Cid-Sueiro, J. ; Dept. de Teoria de la Senal y Comunicaciones e Ing. Telematica, Univ. de Valiadolid, Spain ; Arribas, J.I. ; Urban-Munoz, S. ; Figueiras-Vidal, A.R.

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

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Neural Networks, IEEE Transactions on  (Volume:10 ,  Issue: 3 )