Efficiency of conformalized ridge regression

Evgeny Burnaev, Vladimir Vovk
Proceedings of The 27th Conference on Learning Theory, PMLR 35:605-622, 2014.

Abstract

Conformal prediction is a method of producing prediction sets that can be applied on top of a wide range of prediction algorithms. The method has a guaranteed coverage probability under the standard IID assumption regardless of whether the assumptions (often considerably more restrictive) of the underlying algorithm are satisfied. However, for the method to be really useful it is desirable that in the case where the assumptions of the underlying algorithm are satisfied, the conformal predictor loses little in efficiency as compared with the underlying algorithm (whereas being a conformal predictor, it has the stronger guarantee of validity). In this paper we explore the degree to which this additional requirement of efficiency is satisfied in the case of Bayesian ridge regression; we find that asymptotically conformal prediction sets differ little from ridge regression prediction intervals when the standard Bayesian assumptions are satisfied.

Cite this Paper

BibTeX
@InProceedings{pmlr-v35-burnaev14, title = {Efficiency of conformalized ridge regression}, author = {Burnaev, Evgeny and Vovk, Vladimir}, booktitle = {Proceedings of The 27th Conference on Learning Theory}, pages = {605--622}, year = {2014}, editor = {Balcan, Maria Florina and Feldman, Vitaly and Szepesvári, Csaba}, volume = {35}, series = {Proceedings of Machine Learning Research}, address = {Barcelona, Spain}, month = {13--15 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v35/burnaev14.pdf}, url = {https://proceedings.mlr.press/v35/burnaev14.html}, abstract = {Conformal prediction is a method of producing prediction sets that can be applied on top of a wide range of prediction algorithms. The method has a guaranteed coverage probability under the standard IID assumption regardless of whether the assumptions (often considerably more restrictive) of the underlying algorithm are satisfied. However, for the method to be really useful it is desirable that in the case where the assumptions of the underlying algorithm are satisfied, the conformal predictor loses little in efficiency as compared with the underlying algorithm (whereas being a conformal predictor, it has the stronger guarantee of validity). In this paper we explore the degree to which this additional requirement of efficiency is satisfied in the case of Bayesian ridge regression; we find that asymptotically conformal prediction sets differ little from ridge regression prediction intervals when the standard Bayesian assumptions are satisfied.} }
Endnote
%0 Conference Paper %T Efficiency of conformalized ridge regression %A Evgeny Burnaev %A Vladimir Vovk %B Proceedings of The 27th Conference on Learning Theory %C Proceedings of Machine Learning Research %D 2014 %E Maria Florina Balcan %E Vitaly Feldman %E Csaba Szepesvári %F pmlr-v35-burnaev14 %I PMLR %P 605--622 %U https://proceedings.mlr.press/v35/burnaev14.html %V 35 %X Conformal prediction is a method of producing prediction sets that can be applied on top of a wide range of prediction algorithms. The method has a guaranteed coverage probability under the standard IID assumption regardless of whether the assumptions (often considerably more restrictive) of the underlying algorithm are satisfied. However, for the method to be really useful it is desirable that in the case where the assumptions of the underlying algorithm are satisfied, the conformal predictor loses little in efficiency as compared with the underlying algorithm (whereas being a conformal predictor, it has the stronger guarantee of validity). In this paper we explore the degree to which this additional requirement of efficiency is satisfied in the case of Bayesian ridge regression; we find that asymptotically conformal prediction sets differ little from ridge regression prediction intervals when the standard Bayesian assumptions are satisfied.
RIS
TY - CPAPER TI - Efficiency of conformalized ridge regression AU - Evgeny Burnaev AU - Vladimir Vovk BT - Proceedings of The 27th Conference on Learning Theory DA - 2014/05/29 ED - Maria Florina Balcan ED - Vitaly Feldman ED - Csaba Szepesvári ID - pmlr-v35-burnaev14 PB - PMLR DP - Proceedings of Machine Learning Research VL - 35 SP - 605 EP - 622 L1 - http://proceedings.mlr.press/v35/burnaev14.pdf UR - https://proceedings.mlr.press/v35/burnaev14.html AB - Conformal prediction is a method of producing prediction sets that can be applied on top of a wide range of prediction algorithms. The method has a guaranteed coverage probability under the standard IID assumption regardless of whether the assumptions (often considerably more restrictive) of the underlying algorithm are satisfied. However, for the method to be really useful it is desirable that in the case where the assumptions of the underlying algorithm are satisfied, the conformal predictor loses little in efficiency as compared with the underlying algorithm (whereas being a conformal predictor, it has the stronger guarantee of validity). In this paper we explore the degree to which this additional requirement of efficiency is satisfied in the case of Bayesian ridge regression; we find that asymptotically conformal prediction sets differ little from ridge regression prediction intervals when the standard Bayesian assumptions are satisfied. ER -
APA
Burnaev, E. & Vovk, V.. (2014). Efficiency of conformalized ridge regression. Proceedings of The 27th Conference on Learning Theory, in Proceedings of Machine Learning Research 35:605-622 Available from https://proceedings.mlr.press/v35/burnaev14.html.

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