On training locally adaptive CP
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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 →ϕ_X(A), that depends explicitly on the object attributes, X. Under certain conditions and if ϕ_X 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 ϕ_X 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.
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