On training locally adaptive CP

We address the problem of making Conformal Prediction (CP) intervals locally adaptive. Most existing methods focus on approximating the object-conditional validity of the intervals by partitioning or re-weighting the calibration set. Our strategy is new and conceptually different. Instead of re-weighting the calibration data, we redefine the conformity measure through a trainable change of variables, A → φX(A), that depends explicitly on the object attributes, X. Under certain conditions and if φX is monotonic in A for any X, the transformations produce prediction intervals that are guaranteed to be marginally valid and have X-dependent sizes. We describe how to parameterize and train φX to maximize the interval efficiency. Contrary to other CP-aware training methods, the objective function is smooth and can be minimized through standard gradient methods without approximations.