Cost functions to estimate a posteriori probabilities in multiclass problems
Jesús Cid‐Sueiro, Juan Ignacio Arribas, S. Urban-Munoz, Aníbal Ramón Figueiras-Vidal · IEEE Transactions on Neural Networks · 1999
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.