Conformal Prediction (CP) algorithms estimate the uncertainty of a prediction
model by calibrating its outputs on labeled data. The same calibration scheme
usually applies to any model and data without modifications. The obtained
prediction intervals are valid by construction but could be inefficient, i.e.
unnecessarily big, if the prediction errors are not uniformly distributed over
the input space.
We present a general scheme to localize the intervals by training the
calibration process. The standard prediction error is replaced by an optimized
distance metric that depends explicitly on the object attributes. Learning the
optimal metric is equivalent to training a Normalizing Flow that acts on the
joint distribution of the errors and the inputs. Unlike the Error Re-weighting
CP algorithm of Papadopoulos et al. (2008), the framework allows estimating the
gap between nominal and empirical conditional validity. The approach is
compatible with existing locally-adaptive CP strategies based on re-weighting
the calibration samples and applies to any point-prediction model without
retraining.

用标定的数据校准预测模型的不确定性，通过训练标定过程以实现区间的本地化，选择适当的距离度量代替标准预测误差，并通过训练来学习最优度量，从而充分应用于现有的局部适应性标定策略，适用于任何点预测模型。