Prediction intervals for neural network models using weighted asymmetric loss functions

TL;DR

This paper introduces a straightforward method for generating prediction intervals for neural network forecasts using weighted asymmetric loss functions, validated on real-world data to produce reliable uncertainty estimates.

Contribution

It presents a novel, mathematically justified approach to estimate prediction intervals with neural networks by employing weighted asymmetric loss functions, extending to parametrized functions.

Findings

Produces reliable prediction intervals in complex scenarios

Effective for deep neural network training

Validated on real-world forecasting tasks

Abstract

We propose a simple and efficient approach to generate a prediction intervals (PI) for approximated and forecasted trends. Our method leverages a weighted asymmetric loss function to estimate the lower and upper bounds of the PI, with the weights determined by its coverage probability. We provide a concise mathematical proof of the method, show how it can be extended to derive PIs for parametrised functions and discuss its effectiveness when training deep neural networks. The presented tests of the method on a real-world forecasting task using a neural network-based model show that it can produce reliable PIs in complex machine learning scenarios.