Cost functions to estimate a posteriori probabilities in multiclass problems

TitleCost functions to estimate a posteriori probabilities in multiclass problems
Publication TypeJournal Article
Year of Publication1999
AuthorsCid-Sueiro, J., J. I. Arribas, S. Urban-Munoz, and A. R. Figueiras-Vidal
JournalIEEE Transactions on Neural Networks
Volume10
Pagination645-656
ISSN10459227
KeywordsCost 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.

URLhttp://www.scopus.com/inward/record.url?eid=2-s2.0-0032643080&partnerID=40&md5=d528195bd6ec84531e59ddd2ececcd46
DOI10.1109/72.761724