Distributional anchor regression

Kook, Lucas; Sick, Beate; Bühlmann, Peter

doi:10.1007/s11222-022-10097-z

Please use this identifier to cite or link to this item: https://doi.org/10.21256/zhaw-27459

Publication type:	Article in scientific journal
Type of review:	Peer review (publication)
Title:	Distributional anchor regression
Authors:	Kook, Lucas Sick, Beate Bühlmann, Peter
et. al:	No
DOI:	10.1007/s11222-022-10097-z 10.21256/zhaw-27459
Published in:	Statistics and Computing
Volume(Issue):	32
Issue:	3
Page(s):	39
Issue Date:	2022
Publisher / Ed. Institution:	Springer
ISSN:	0960-3174 1573-1375
Language:	English
Subjects:	Anchor regression; Covariate shift; Diluted causality; Distributional regression; Out-of-distribution generalization; Transformation models
Subject (DDC):	510: Mathematics
Abstract:	Prediction models often fail if train and test data do not stem from the same distribution. Out-of-distribution (OOD) generalization to unseen, perturbed test data is a desirable but difficult-to-achieve property for prediction models and in general requires strong assumptions on the data generating process (DGP). In a causally inspired perspective on OOD generalization, the test data arise from a specific class of interventions on exogenous random variables of the DGP, called anchors. Anchor regression models, introduced by Rothenhäusler et al. (J R Stat Soc Ser B 83(2):215-246, 2021. 10.1111/rssb.12398), protect against distributional shifts in the test data by employing causal regularization. However, so far anchor regression has only been used with a squared-error loss which is inapplicable to common responses such as censored continuous or ordinal data. Here, we propose a distributional version of anchor regression which generalizes the method to potentially censored responses with at least an ordered sample space. To this end, we combine a flexible class of parametric transformation models for distributional regression with an appropriate causal regularizer under a more general notion of residuals. In an exemplary application and several simulation scenarios we demonstrate the extent to which OOD generalization is possible.
URI:	https://digitalcollection.zhaw.ch/handle/11475/27459
Fulltext version:	Published version
License (according to publishing contract):	CC BY 4.0: Attribution 4.0 International
Departement:	School of Engineering
Organisational Unit:	Institute of Data Analysis and Process Design (IDP)
Appears in collections:	Publikationen School of Engineering

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Kook, L., Sick, B., & Bühlmann, P. (2022). Distributional anchor regression. Statistics and Computing, 32(3), 39. https://doi.org/10.1007/s11222-022-10097-z

Kook, L., Sick, B. and Bühlmann, P. (2022) ‘Distributional anchor regression’, Statistics and Computing, 32(3), p. 39. Available at: https://doi.org/10.1007/s11222-022-10097-z.

L. Kook, B. Sick, and P. Bühlmann, “Distributional anchor regression,” Statistics and Computing, vol. 32, no. 3, p. 39, 2022, doi: 10.1007/s11222-022-10097-z.

KOOK, Lucas, Beate SICK und Peter BÜHLMANN, 2022. Distributional anchor regression. Statistics and Computing. 2022. Bd. 32, Nr. 3, S. 39. DOI 10.1007/s11222-022-10097-z

Kook, Lucas, Beate Sick, and Peter Bühlmann. 2022. “Distributional Anchor Regression.” Statistics and Computing 32 (3): 39. https://doi.org/10.1007/s11222-022-10097-z.

Kook, Lucas, et al. “Distributional Anchor Regression.” Statistics and Computing, vol. 32, no. 3, 2022, p. 39, https://doi.org/10.1007/s11222-022-10097-z.