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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
Published in: Statistics and Computing
Volume(Issue): 32
Issue: 3
Page(s): 39
Issue Date: 2022
Publisher / Ed. Institution: Springer
ISSN: 0960-3174
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.
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.
Kook, L., Sick, B. and Bühlmann, P. (2022) ‘Distributional anchor regression’, Statistics and Computing, 32(3), p. 39. Available at:
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.
Kook, Lucas, et al. “Distributional Anchor Regression.” Statistics and Computing, vol. 32, no. 3, 2022, p. 39,

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