Beta Distributional Neural Networks for Bounded Outcome Prediction

Abstract

This paper presents a new neural modeling system, named the Beta-Distributional Neural Network (BDNN), which is aimed at predicting restricted outcomes over the open unit interval (0,1). In contrast to the traditional neural networks, which produce deterministic point estimates, the proposed model provides direct predictions of the two shape parameters of the beta distribution (  and ), and thus, predictive mean and uncertainty can be estimated simultaneously. This is to achieve statistical coherence and computational stability, which is trained through maximum likelihood estimation by minimizing the negative log-likelihood. It is tested on BDNN using synthetic data sets, which have been built based on the data-generating curves, both linear and nonlinear, as well as a real-world colon cancer drug-response dataset. It makes comparative studies using ordinary least squares regression, classical beta regression and traditional feedforward neural network. Empirical findings prove that BDNN always has better predictive accuracy in terms of reduced RMSE and MAE values and has better probabilistic calibration based on negative log-likelihood. These results indicate the adequacy of incorporating distributional modelling with deep neural structures in the prediction of limited outcomes in medical and applied research areas.