Dual Accuracy-Quality-Driven Neural Network for Prediction Interval Generation

Accurate uncertainty quantification is necessary to enhance the reliability of deep learning models in real-world applications. In the case of regression tasks, prediction intervals (PIs) should be provided along with the deterministic predictions of deep learning models. Such PIs are useful or "high-quality'' as long as they are sufficiently narrow and capture most of the probability density. In this paper, we present a method to learn prediction intervals for regression-based neural networks automatically in addition to the conventional target predictions. In particular, we train two companion neural networks: one that uses one output, the target estimate, and another that uses two outputs, the upper and lower bounds of the corresponding PI. Our main contribution is the design of a loss function for the PI-generation network that takes into account the output of the target-estimation network and has two optimization objectives: minimizing the mean prediction interval width and ensuring the PI integrity using constraints that maximize the prediction interval probability coverage implicitly. Both objectives are balanced within the loss function using a self-adaptive coefficient. Furthermore, we apply a Monte Carlo-based approach that evaluates the model uncertainty in the learned PIs. Experiments using a synthetic dataset, six benchmark datasets, and a real-world crop yield prediction dataset showed that our method was able to maintain a nominal probability coverage and produce narrower PIs without detriment to its target estimation accuracy when compared to those PIs generated by three state-of-the-art neural-network-based methods.