Tight Prediction Intervals Using Expanded Interval Minimization
This addresses the need for more accurate uncertainty quantification in regression for applications with non-standard data distributions, though it is an incremental improvement over existing techniques.
The paper tackled the problem of generating prediction intervals for regression with asymmetric error distributions by introducing Expanded Interval Minimization (EIM), a loss function for neural networks, resulting in intervals that are on average 1.37x tighter than prior methods.
Prediction intervals are a valuable way of quantifying uncertainty in regression problems. Good prediction intervals should be both correct, containing the actual value between the lower and upper bound at least a target percentage of the time; and tight, having a small mean width of the bounds. Many prior techniques for generating prediction intervals make assumptions on the distribution of error, which causes them to work poorly for problems with asymmetric distributions. This paper presents Expanded Interval Minimization (EIM), a novel loss function for generating prediction intervals using neural networks. This loss function uses minibatch statistics to estimate the coverage and optimize the width of the prediction intervals. It does not make the same assumptions on the distributions of data and error as prior work. We compare to three published techniques and show EIM produces on average 1.37x tighter prediction intervals and in the worst case 1.06x tighter intervals across two large real-world datasets and varying coverage levels.