With the emergence of online learning systems which generate ever-growing amounts of data, quantifying the uncertainty in predictions regarding the system's operation is becoming increasingly more important. Prediction intervals offer a powerful tool for assessing prediction uncertainty in artificial neural network applications; nevertheless, little work has been conducted on constructing prediction intervals for online learning applications. In this work, we propose a hybrid approach which employs artificial neural networks to directly estimate prediction intervals for both batch and online approximation scenarios. The aim of the approach is to provide high-quality prediction intervals, combining high coverage probability for future observations with small and thus informative interval widths. Compared with three popular methods for offline construction of prediction intervals, the proposed approach demonstrates a strong capacity for reliably representing prediction uncertainty in real-world regression applications. The approach is extended to adaptive approximation, whereby four online learning schemes are proposed to iteratively update prediction intervals based on recent measurements, requiring a reduced computational cost compared to offline approximation. The four online prediction intervals methods are compared over two synthetic and one real-world regression datasets, whereby data arrive in a sequential manner. Our results suggest the potential of an online learning scheme relying on a human-like memory mechanism, to construct high-quality online prediction intervals, capable of adapting to dynamic changes in data patterns. The proposed method is associated with low computational cost-an attractive feature for online learning applications requiring real-time performance.
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