  We discuss theoretical aspects of the product rule for classification
problems in supervised machine learning for the case of combining classifiers.
We show that (1) the product rule arises from the MAP classifier supposing
equivalent priors and conditional independence given a class; (2) under some
conditions, the product rule is equivalent to minimizing the sum of the squared
distances to the respective centers of the classes related with different
features, such distances being weighted by the spread of the classes; (3)
observing some hypothesis, the product rule is equivalent to concatenating the
vectors of features.
