The Statistical Scope of Multicalibration

Georgy Noarov, Aaron Roth
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:26283-26310, 2023.

Abstract

We make a connection between multicalibration and property elicitation and show that (under mild technical conditions) it is possible to produce a multicalibrated predictor for a continuous scalar property $\Gamma$ if and only if $\Gamma$ is elicitable. On the negative side, we show that for non-elicitable continuous properties there exist simple data distributions on which even the true distributional predictor is not calibrated. On the positive side, for elicitable $\Gamma$, we give simple canonical algorithms for the batch and the online adversarial setting, that learn a $\Gamma$-multicalibrated predictor. This generalizes past work on multicalibrated means and quantiles, and in fact strengthens existing online quantile multicalibration results. To further counter-weigh our negative result, we show that if a property $\Gamma^1$ is not elicitable by itself, but is elicitable conditionally on another elicitable property $\Gamma^0$, then there is a canonical algorithm that jointly multicalibrates $\Gamma^1$ and $\Gamma^0$; this generalizes past work on mean-moment multicalibration. Finally, as applications of our theory, we provide novel algorithmic and impossibility results for fair (multicalibrated) risk assessment.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-noarov23a, title = {The Statistical Scope of Multicalibration}, author = {Noarov, Georgy and Roth, Aaron}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {26283--26310}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/noarov23a/noarov23a.pdf}, url = {https://proceedings.mlr.press/v202/noarov23a.html}, abstract = {We make a connection between multicalibration and property elicitation and show that (under mild technical conditions) it is possible to produce a multicalibrated predictor for a continuous scalar property $\Gamma$ if and only if $\Gamma$ is elicitable. On the negative side, we show that for non-elicitable continuous properties there exist simple data distributions on which even the true distributional predictor is not calibrated. On the positive side, for elicitable $\Gamma$, we give simple canonical algorithms for the batch and the online adversarial setting, that learn a $\Gamma$-multicalibrated predictor. This generalizes past work on multicalibrated means and quantiles, and in fact strengthens existing online quantile multicalibration results. To further counter-weigh our negative result, we show that if a property $\Gamma^1$ is not elicitable by itself, but is elicitable conditionally on another elicitable property $\Gamma^0$, then there is a canonical algorithm that jointly multicalibrates $\Gamma^1$ and $\Gamma^0$; this generalizes past work on mean-moment multicalibration. Finally, as applications of our theory, we provide novel algorithmic and impossibility results for fair (multicalibrated) risk assessment.} }
Endnote
%0 Conference Paper %T The Statistical Scope of Multicalibration %A Georgy Noarov %A Aaron Roth %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-noarov23a %I PMLR %P 26283--26310 %U https://proceedings.mlr.press/v202/noarov23a.html %V 202 %X We make a connection between multicalibration and property elicitation and show that (under mild technical conditions) it is possible to produce a multicalibrated predictor for a continuous scalar property $\Gamma$ if and only if $\Gamma$ is elicitable. On the negative side, we show that for non-elicitable continuous properties there exist simple data distributions on which even the true distributional predictor is not calibrated. On the positive side, for elicitable $\Gamma$, we give simple canonical algorithms for the batch and the online adversarial setting, that learn a $\Gamma$-multicalibrated predictor. This generalizes past work on multicalibrated means and quantiles, and in fact strengthens existing online quantile multicalibration results. To further counter-weigh our negative result, we show that if a property $\Gamma^1$ is not elicitable by itself, but is elicitable conditionally on another elicitable property $\Gamma^0$, then there is a canonical algorithm that jointly multicalibrates $\Gamma^1$ and $\Gamma^0$; this generalizes past work on mean-moment multicalibration. Finally, as applications of our theory, we provide novel algorithmic and impossibility results for fair (multicalibrated) risk assessment.
APA
Noarov, G. & Roth, A.. (2023). The Statistical Scope of Multicalibration. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:26283-26310 Available from https://proceedings.mlr.press/v202/noarov23a.html.

Related Material