Adaptive, Distribution-Free Prediction Intervals for Deep Networks

TL;DR

This paper introduces distribution-free, guaranteed-performance prediction intervals for deep neural networks using conformal inference and a novel loss function, improving reliability without sacrificing accuracy.

Contribution

It presents a new neural network approach that outputs multiple values, enabling valid prediction intervals with minimal assumptions and no accuracy loss.

Findings

Methods provide finite-sample coverage guarantees.

Approach is easy to implement and improves over existing methods.

Applicable to both simulated and real datasets.

Abstract

The machine learning literature contains several constructions for prediction intervals that are intuitively reasonable but ultimately ad-hoc in that they do not come with provable performance guarantees. We present methods from the statistics literature that can be used efficiently with neural networks under minimal assumptions with guaranteed performance. We propose a neural network that outputs three values instead of a single point estimate and optimizes a loss function motivated by the standard quantile regression loss. We provide two prediction interval methods with finite sample coverage guarantees solely under the assumption that the observations are independent and identically distributed. The first method leverages the conformal inference framework and provides average coverage. The second method provides a new, stronger guarantee by conditioning on the observed data. Lastly, our loss function does not compromise the predictive accuracy of the network like other prediction interval methods. We demonstrate the ease of use of our procedures as well as its improvements over other methods on both simulated and real data. As most deep networks can easily be modified by our method to output predictions with valid prediction intervals, its use should become standard practice, much like reporting standard errors along with mean estimates.