Supervised estimation of random variables taking on values in finite, ordered sets

Several problems require the estimation of discrete random variables whose values can be put in a one-to-one ordered correspondence with a subset of the natural numbers. This happens whenever quantities are involved that represent integer items, or have been quantized on a fixed number of levels, or correspond to “graded” linguistic values. In this paper we propose a correct probabilistic approach to this type of problems, which fully exploits all the available prior knowledge about their own structure. The method can be directly applied to standard feedforward networks while keeping local computation of both outputs and error signals. According to these guidelines, we successfully devised a neural implementation of a complex pre-processing algorithm using very poor resolution on the computing elements in the network