On the Relative Expressiveness of Bayesian and Neural Networks
This work addresses a foundational theoretical problem in machine learning by clarifying the relative capabilities of two major model types, with incremental improvements for Bayesian networks.
The paper tackled the problem of comparing the expressiveness of neural networks and Bayesian networks, showing that neural networks are more expressive than Bayesian network queries, and proposed a testing operator augmentation to make Bayesian networks universal approximators.
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 marginal 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 marginal queries to become "universal approximators."