On training locally adaptive CP

Nicolo Colombo
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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v204-colombo23a, title = {On training locally adaptive CP}, author = {Colombo, Nicolo}, booktitle = {Proceedings of the Twelfth Symposium on Conformal and Probabilistic Prediction with Applications}, pages = {384--398}, year = {2023}, editor = {Papadopoulos, Harris and Nguyen, Khuong An and Boström, Henrik and Carlsson, Lars}, volume = {204}, series = {Proceedings of Machine Learning Research}, month = {13--15 Sep}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v204/colombo23a/colombo23a.pdf}, url = {https://proceedings.mlr.press/v204/colombo23a.html}, 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.} }
Endnote
%0 Conference Paper %T On training locally adaptive CP %A Nicolo Colombo %B Proceedings of the Twelfth Symposium on Conformal and Probabilistic Prediction with Applications %C Proceedings of Machine Learning Research %D 2023 %E Harris Papadopoulos %E Khuong An Nguyen %E Henrik Boström %E Lars Carlsson %F pmlr-v204-colombo23a %I PMLR %P 384--398 %U https://proceedings.mlr.press/v204/colombo23a.html %V 204 %X 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.
APA
Colombo, N.. (2023). On training locally adaptive CP. Proceedings of the Twelfth Symposium on Conformal and Probabilistic Prediction with Applications, in Proceedings of Machine Learning Research 204:384-398 Available from https://proceedings.mlr.press/v204/colombo23a.html.

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