Abstract
The prediction interval (PI) is an important research topic in reliability analyses and decision support systems. Data size and computation costs are two of the issues which may hamper the construction of PIs. This paper proposes an all-batch (AB) loss function for constructing high quality PIs. Taking the full advantage of the likelihood principle, the proposed loss makes it possible to train PI generation models using the gradient descent (GD) method for both small and large batches of samples. With the structure of dual feedforward neural networks (FNNs), a high-quality PI generation framework is introduced, which can be adapted to a variety of problems including regression analysis. Numerical experiments were conducted on the benchmark datasets; the results show that higher-quality PIs were achieved using the proposed scheme. Its reliability and stability were also verified in comparison with various state-of-the-art PI construction methods.
Highlights
The prediction interval (PI) is widely used to evaluate uncertainty
Different from the confidence interval (CI) which only relies on statistical analyses of the observed data, the PI describes the uncertainty by means of predictions, which cover estimates of both model uncertainty and data uncertainty [1]
The penalty term adopted in the AB loss is conducive to guiding the update of network parameters in the direction of improving PI coverage probability (PICP)
Summary
The prediction interval (PI) is widely used to evaluate uncertainty. Different from the confidence interval (CI) which only relies on statistical analyses of the observed data, the PI describes the uncertainty by means of predictions, which cover estimates of both model uncertainty and data uncertainty [1]. Plenty of models have been proposed to construct PIs through FNNs and have achieved remarkable results, many of them may be unsuitable for real-world tasks due to high computational costs and complex assumptions. Heskes [14], Carney et al [15] and Errouissi et al [16] adopted the bootstrap method to construct PIs with FNNs. Bootstrap procedures are useful for uncertainty estimates, and are widely used in many fields, as they provide reliable solutions to obtain the predictive distribution of the output variables in NNs [17]. To address the aforementioned problems, this paper proposes an all-batch (AB) loss function to construct high-quality PIs. On the basis of making full use of the advantages of likelihood principles, the proposed AB loss function can be applied to both small and large batches of samples.
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