Conformal Prediction Intervals for Neural Networks Using Cross Validation

TL;DR

This paper introduces a $k$-fold cross-validation based method for constructing prediction intervals for neural networks, which tends to produce narrower intervals with reliable coverage, especially with limited data.

Contribution

The paper proposes a novel $k$-fold prediction interval method for neural networks, improving interval narrowness while maintaining coverage compared to existing split conformal methods.

Findings

The $k$-fold method produces narrower prediction intervals than the split conformal method.

The method maintains the same coverage probability as existing approaches.

It is particularly effective with limited training data.

Abstract

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.