Constructing Prediction Intervals with Neural Networks: An Empirical Evaluation of Bootstrapping and Conformal Inference Methods

TL;DR

This paper evaluates methods for constructing prediction intervals with neural networks, focusing on bootstrapping and conformal inference, and provides practical guidance for optimizing their performance across various data sets.

Contribution

It offers a comprehensive empirical comparison of PI construction methods for ANNs, highlighting how network design choices influence PI quality and identifying the cross-conformal method as a balanced approach.

Findings

Cross-conformal method offers optimal trade-off between coverage and efficiency.

Network design choices significantly impact PI performance.

Conformal inference methods generally outperform bootstrapping in this context.

Abstract

Artificial neural networks (ANNs) are popular tools for accomplishing many machine learning tasks, including predicting continuous outcomes. However, the general lack of confidence measures provided with ANN predictions limit their applicability. Supplementing point predictions with prediction intervals (PIs) is common for other learning algorithms, but the complex structure and training of ANNs renders constructing PIs difficult. This work provides the network design choices and inferential methods for creating better performing PIs with ANNs. A two-step experiment is executed across 11 data sets, including an imaged-based data set. Two distribution-free methods for constructing PIs, bootstrapping and conformal inference, are considered. The results of the first experimental step reveal that the choices inherent to building an ANN affect PI performance. Guidance is provided for optimizing PI performance with respect to each network feature and PI method. In the second step, 20 algorithms for constructing PIs, each using the principles of bootstrapping or conformal inference, are implemented to determine which provides the best performance while maintaining reasonable computational burden. In general, this trade-off is optimized when implementing the cross-conformal method, which maintained interval coverage and efficiency with decreased computational burden.