Categorical Aspects of Parameter Learning
  Parameter learning is the technique for obtaining the probabilistic
parameters in conditional probability tables in Bayesian networks from tables
with (observed) data --- where it is assumed that the underlying graphical
structure is known. There are basically two ways of doing so, referred to as
maximal likelihood estimation (MLE) and as Bayesian learning. This paper
provides a categorical analysis of these two techniques and describes them in
terms of basic properties of the multiset monad M, the distribution monad D and
the Giry monad G. In essence, learning is about the reltionships between
multisets (used for counting) on the one hand and probability distributions on
the other. These relationsips will be described as suitable natural
transformations.
