Bayesian Networks as Classifiers

Abstract

A coalgebraic description of (discrete) Bayesian networks is presented. The coalgebra map representing a network sends a node to its set of predecessors, together with the associated conditional probability tables. We use this descrip-tion to describe the semantics of a network in terms of various (discrete) probabil-ity distributions associated with a node: local, joint, and conditional distributions. In the background simple Python scripts are used to compute these distributions. The local and joint distributions are defined 'recursively', following the coalge-bra structure. Underlying this approach are some basic properties of the (discrete probability) distribution monad. In the end we identify some new structure of the distribution monad and isolate it in what we call a 'relatively monoidal'.