A Connection between Feed-Forward Neural Networks and Probabilistic Graphical Models

TL;DR

This paper reveals that feed-forward neural networks can be viewed as approximations of Bayesian networks, leading to new learning algorithms and improved performance in vision tasks like classification and segmentation.

Contribution

It establishes a novel theoretical connection between FFNs and Bayesian networks, enabling new learning methods and better generalization in vision applications.

Findings

BNs learned statistically outperform FFNs in accuracy.

BNs demonstrate better generalization capabilities.

Proposed methods improve performance on CIFAR-10 and Weizmann Horse datasets.

Abstract

Two of the most popular modelling paradigms in computer vision are feed-forward neural networks (FFNs) and probabilistic graphical models (GMs). Various connections between the two have been studied in recent works, such as e.g. expressing mean-field based inference in a GM as an FFN. This paper establishes a new connection between FFNs and GMs. Our key observation is that any FFN implements a certain approximation of a corresponding Bayesian network (BN). We characterize various benefits of having this connection. In particular, it results in a new learning algorithm for BNs. We validate the proposed methods for a classification problem on CIFAR-10 dataset and for binary image segmentation on Weizmann Horse dataset. We show that statistically learned BNs improve performance, having at the same time essentially better generalization capability, than their FFN counterparts.