# On the Relative Expressiveness of Bayesian and Neural Networks

## TL;DR

This paper compares the expressiveness of neural networks and Bayesian networks, showing neural networks are more expressive and proposing an augmentation to Bayesian networks to enhance their approximation capabilities.

## Contribution

It identifies key differences in the functions computed by neural and Bayesian networks and introduces a testing operator to make Bayesian networks more universally approximating.

## Key findings

- Neural networks are more expressive than Bayesian network queries.
- A simple augmentation can make Bayesian networks universal approximators.
- The proposed method enhances Bayesian networks' functional approximation capabilities.

## Abstract

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."