Bayesian Perceptron: Towards fully Bayesian Neural Networks
This work addresses the need for uncertainty quantification in neural networks, offering a foundational step towards fully Bayesian neural networks, though it is incremental as it focuses on a perceptron model.
The paper tackles the problem of neural networks providing only point estimates without uncertainty quantification by proposing a Bayesian perceptron that performs training and predictions in closed-form, requiring no gradient calculations and enabling sequential learning.
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.