Geometric Implications of the Naive Bayes Assumption
  A naive (or Idiot) Bayes network is a network with a single hypothesis node
and several observations that are conditionally independent given the
hypothesis. We recently surveyed a number of members of the UAI community and
discovered a general lack of understanding of the implications of the Naive
Bayes assumption on the kinds of problems that can be solved by these networks.
It has long been recognized [Minsky 61] that if observations are binary, the
decision surfaces in these networks are hyperplanes. We extend this result
(hyperplane separability) to Naive Bayes networks with m-ary observations. In
addition, we illustrate the effect of observation-observation dependencies on
decision surfaces. Finally, we discuss the implications of these results on
knowledge acquisition and research in learning.
