Finite sample valid probabilistic inference on quantile regression

Leonardo Cella
Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications, PMLR 215:109-118, 2023.

Abstract

In most applications, uncertainty quantification in quantile regression take the form of set estimates for the regression coefficients. However, often a more informative type of uncertainty quantification is desired where other inference-related tasks can be performed, such as the assignment of (imprecise) probabilities to assertions of interest about (any feature of) the regression coefficients. Validity of these probabilities, in the sense that their values are well-calibrated in a frequentist sense, is fundamental to the trustworthiness of the drawn conclusions. This paper presents a nonparametric Inferential Model (IM) construction that offers provably valid probabilistic uncertainty quantification in quantile regression, even in finite sample settings. It is also shown that this IM can be used to derive finite sample confidence regions for (any feature of) the regression coefficients. As a result, regardless of the type of uncertainty quantification desired, the proposed IM offers an appealing solution to quantile regression problems.

Cite this Paper

BibTeX
@InProceedings{pmlr-v215-cella23a, title = {Finite sample valid probabilistic inference on quantile regression}, author = {Cella, Leonardo}, booktitle = {Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications}, pages = {109--118}, year = {2023}, editor = {Miranda, Enrique and Montes, Ignacio and Quaeghebeur, Erik and Vantaggi, Barbara}, volume = {215}, series = {Proceedings of Machine Learning Research}, month = {11--14 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v215/cella23a/cella23a.pdf}, url = {https://proceedings.mlr.press/v215/cella23a.html}, abstract = {In most applications, uncertainty quantification in quantile regression take the form of set estimates for the regression coefficients. However, often a more informative type of uncertainty quantification is desired where other inference-related tasks can be performed, such as the assignment of (imprecise) probabilities to assertions of interest about (any feature of) the regression coefficients. Validity of these probabilities, in the sense that their values are well-calibrated in a frequentist sense, is fundamental to the trustworthiness of the drawn conclusions. This paper presents a nonparametric Inferential Model (IM) construction that offers provably valid probabilistic uncertainty quantification in quantile regression, even in finite sample settings. It is also shown that this IM can be used to derive finite sample confidence regions for (any feature of) the regression coefficients. As a result, regardless of the type of uncertainty quantification desired, the proposed IM offers an appealing solution to quantile regression problems.} }
Endnote
%0 Conference Paper %T Finite sample valid probabilistic inference on quantile regression %A Leonardo Cella %B Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications %C Proceedings of Machine Learning Research %D 2023 %E Enrique Miranda %E Ignacio Montes %E Erik Quaeghebeur %E Barbara Vantaggi %F pmlr-v215-cella23a %I PMLR %P 109--118 %U https://proceedings.mlr.press/v215/cella23a.html %V 215 %X In most applications, uncertainty quantification in quantile regression take the form of set estimates for the regression coefficients. However, often a more informative type of uncertainty quantification is desired where other inference-related tasks can be performed, such as the assignment of (imprecise) probabilities to assertions of interest about (any feature of) the regression coefficients. Validity of these probabilities, in the sense that their values are well-calibrated in a frequentist sense, is fundamental to the trustworthiness of the drawn conclusions. This paper presents a nonparametric Inferential Model (IM) construction that offers provably valid probabilistic uncertainty quantification in quantile regression, even in finite sample settings. It is also shown that this IM can be used to derive finite sample confidence regions for (any feature of) the regression coefficients. As a result, regardless of the type of uncertainty quantification desired, the proposed IM offers an appealing solution to quantile regression problems.
APA
Cella, L.. (2023). Finite sample valid probabilistic inference on quantile regression. Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications, in Proceedings of Machine Learning Research 215:109-118 Available from https://proceedings.mlr.press/v215/cella23a.html.

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