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.

我们开发了一种在特征空间的所有区域具有用户指定的覆盖水平的预测区间生成方法，称为条件覆盖。我们发现传统的分位数回归可能具有较差的条件覆盖，并通过修改损失函数来解决这个问题，从而提高了实验室中的条件覆盖。

通过正交分位数回归改善条件覆盖率