Abstract
We consider a multi-class pattern recognition problem with linearly ordered labels and a loss function, which is a sum of squared deviations of decisions from true classes. It is proved that the optimal, in the Bayesian sense, decision rule is the a posteriori mean, which is then rounded to the nearest integer. Then, the plug-in type estimator of the optimal decision rule is proposed. We also investigate its asymptotic properties. Finally, we discuss briefly the structure of a neural net, which approximates the optimal decision rule.
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