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On training locally adaptive CP
Proceedings of the Twelfth Symposium on Conformal
and Probabilistic Prediction with Applications, PMLR 204:384-398, 2023.
Abstract
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 → $\phi$X(A), that
depends explicitly on the object attributes,
X. Under certain conditions and if $\phi$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 $\phi$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.