Mondrian conformal predictive distributions

Henrik Boström, Ulf Johansson, Tuwe Löfström
Proceedings of the Tenth Symposium on Conformal and Probabilistic Prediction and Applications, PMLR 152:24-38, 2021.

Abstract

The distributions output by a standard (non-normalized) conformal predictive system all have the same shape but differ in location, while a normalized conformal predictive system outputs distributions that differ also in shape, through rescaling. An approach to further increasing the flexibility of the framework is proposed, called \emph{Mondrian conformal predictive distributions}, which are (standard or normalized) conformal predictive distributions formed from multiple Mondrian categories. The effectiveness of the approach is demonstrated with an application to regression forests. By forming categories through binning of the predictions, it is shown that for this model class, the use of Mondrian conformal predictive distributions significantly outperforms the use of both standard and normalized conformal predictive distributions with respect to the continuous- ranked probability score. It is further shown that the use of Mondrian conformal predictive distributions results in as tight prediction intervals as produced by normalized conformal regressors, while improving upon the point predictions of the underlying regression forest.

Cite this Paper

BibTeX
@InProceedings{pmlr-v152-bostrom21a, title = {Mondrian conformal predictive distributions}, author = {Bostr\"{o}m, Henrik and Johansson, Ulf and L\"{o}fstr\"{o}m, Tuwe}, booktitle = {Proceedings of the Tenth Symposium on Conformal and Probabilistic Prediction and Applications}, pages = {24--38}, year = {2021}, editor = {Carlsson, Lars and Luo, Zhiyuan and Cherubin, Giovanni and An Nguyen, Khuong}, volume = {152}, series = {Proceedings of Machine Learning Research}, month = {08--10 Sep}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v152/bostrom21a/bostrom21a.pdf}, url = {https://proceedings.mlr.press/v152/bostrom21a.html}, abstract = {The distributions output by a standard (non-normalized) conformal predictive system all have the same shape but differ in location, while a normalized conformal predictive system outputs distributions that differ also in shape, through rescaling. An approach to further increasing the flexibility of the framework is proposed, called \emph{Mondrian conformal predictive distributions}, which are (standard or normalized) conformal predictive distributions formed from multiple Mondrian categories. The effectiveness of the approach is demonstrated with an application to regression forests. By forming categories through binning of the predictions, it is shown that for this model class, the use of Mondrian conformal predictive distributions significantly outperforms the use of both standard and normalized conformal predictive distributions with respect to the continuous- ranked probability score. It is further shown that the use of Mondrian conformal predictive distributions results in as tight prediction intervals as produced by normalized conformal regressors, while improving upon the point predictions of the underlying regression forest.} }
Endnote
%0 Conference Paper %T Mondrian conformal predictive distributions %A Henrik Boström %A Ulf Johansson %A Tuwe Löfström %B Proceedings of the Tenth Symposium on Conformal and Probabilistic Prediction and Applications %C Proceedings of Machine Learning Research %D 2021 %E Lars Carlsson %E Zhiyuan Luo %E Giovanni Cherubin %E Khuong An Nguyen %F pmlr-v152-bostrom21a %I PMLR %P 24--38 %U https://proceedings.mlr.press/v152/bostrom21a.html %V 152 %X The distributions output by a standard (non-normalized) conformal predictive system all have the same shape but differ in location, while a normalized conformal predictive system outputs distributions that differ also in shape, through rescaling. An approach to further increasing the flexibility of the framework is proposed, called \emph{Mondrian conformal predictive distributions}, which are (standard or normalized) conformal predictive distributions formed from multiple Mondrian categories. The effectiveness of the approach is demonstrated with an application to regression forests. By forming categories through binning of the predictions, it is shown that for this model class, the use of Mondrian conformal predictive distributions significantly outperforms the use of both standard and normalized conformal predictive distributions with respect to the continuous- ranked probability score. It is further shown that the use of Mondrian conformal predictive distributions results in as tight prediction intervals as produced by normalized conformal regressors, while improving upon the point predictions of the underlying regression forest.
APA
Boström, H., Johansson, U. & Löfström, T.. (2021). Mondrian conformal predictive distributions. Proceedings of the Tenth Symposium on Conformal and Probabilistic Prediction and Applications, in Proceedings of Machine Learning Research 152:24-38 Available from https://proceedings.mlr.press/v152/bostrom21a.html.

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