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Conformal Prediction Intervals for Neural Networks Using Cross Validation

Neural networks are among the most powerful nonlinear models used to address supervised learning problems. Similar to most machine learning algorithms, neural networks produce point predictions and do not provide any prediction interval which includes an unobserved response value with a specified probability. In this paper, we proposed the $k$-fold prediction interval method to construct prediction intervals for neural networks based on $k$-fold cross validation. Simulation studies and analysis of 10 real datasets are used to compare the finite-sample properties of the prediction intervals produced by the proposed method and the split conformal (SC) method. The results suggest that the proposed method tends to produce narrower prediction intervals compared to the SC method while maintaining the same coverage probability. Our experimental results also reveal that the proposed $k$-fold prediction interval method produces effective prediction intervals and is especially advantageous relative to competing approaches when the number of training observations is limited.