Cost functions to estimate a posteriori probabilities in multiclassproblems |
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Authors: | Cid-Sueiro J. Arribas J.I. Urban-Munoz S. Figueiras-Vidal A.R. |
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Affiliation: | Dept. de Teoria de la Senal y Comunicaciones e Ing. Telematica, Univ. de Valiadolid. |
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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. |
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