Bayesian Perceptron: Towards fully Bayesian Neural Networks

TL;DR

This paper introduces a fully Bayesian perceptron model that provides uncertainty quantification in neural network predictions using closed-form Bayesian inference, avoiding expensive computations.

Contribution

It presents a novel Bayesian perceptron framework with analytical solutions for training and prediction, enabling efficient and sequential Bayesian learning.

Findings

Provides closed-form expressions for Bayesian perceptron predictions

Enables uncertainty quantification in neural network outputs

Supports sequential learning without gradient computations

Abstract

Artificial neural networks (NNs) have become the de facto standard in machine learning. They allow learning highly nonlinear transformations in a plethora of applications. However, NNs usually only provide point estimates without systematically quantifying corresponding uncertainties. In this paper a novel approach towards fully Bayesian NNs is proposed, where training and predictions of a perceptron are performed within the Bayesian inference framework in closed-form. The weights and the predictions of the perceptron are considered Gaussian random variables. Analytical expressions for predicting the perceptron's output and for learning the weights are provided for commonly used activation functions like sigmoid or ReLU. This approach requires no computationally expensive gradient calculations and further allows sequential learning.