On the Relative Expressiveness of Bayesian and Neural Networks

A neural network computes a function. A central property of neural networks is that they are “universal approximators:” for a given continuous function, there exists a neural network that can approximate it arbitrarily well, given enough neurons (and some additional assumptions). In contrast, a Bayesian network is a model, but each of its queries can be viewed as computing a function. In this paper, we identify some key distinctions between the functions computed by neural networks and those by Bayesian network queries, showing that the former are more expressive than the latter. Moreover, we propose a simple augmentation to Bayesian networks (a testing operator), which enables their queries to become “universal approximators” as well.