Improving Conditional Coverage via Orthogonal Quantile Regression

TL;DR

This paper introduces an orthogonal quantile regression method that improves the accuracy of prediction intervals' conditional coverage by promoting independence between interval size and miscoverage indicators.

Contribution

It proposes a modified loss function for quantile regression that enhances conditional coverage accuracy by enforcing orthogonality between interval size and miscoverage indicators.

Findings

Modified loss function improves conditional coverage in experiments

New metrics effectively evaluate dependence between interval size and miscoverage

Method outperforms traditional quantile regression in finite-sample scenarios

Abstract

We develop a method to generate prediction intervals that have a user-specified coverage level across all regions of feature-space, a property called conditional coverage. A typical approach to this task is to estimate the conditional quantiles with quantile regression -- it is well-known that this leads to correct coverage in the large-sample limit, although it may not be accurate in finite samples. We find in experiments that traditional quantile regression can have poor conditional coverage. To remedy this, we modify the loss function to promote independence between the size of the intervals and the indicator of a miscoverage event. For the true conditional quantiles, these two quantities are independent (orthogonal), so the modified loss function continues to be valid. Moreover, we empirically show that the modified loss function leads to improved conditional coverage, as evaluated by several metrics. We also introduce two new metrics that check conditional coverage by looking at the strength of the dependence between the interval size and the indicator of miscoverage.