Open access
Date
2021-04Type
- Journal Article
Abstract
We consider the problem of predicting a response variable from a set of covariates on a data set that differs in distribution from the training data. Causal parameters are optimal in terms of predictive accuracy if in the new distribution either many variables are affected by interventions or only some variables are affected, but the perturbations are strong. If the training and test distributions differ by a shift, causal parameters might be too conservative to perform well on the above task. This motivates anchor regression, a method that makes use of exogenous variables to solve a relaxation of the 'causal' minimax problem by considering a modification of the least-squares loss. The procedure naturally provides an interpolation between the solutions of ordinary least squares (OLS) and two-stage least squares. We prove that the estimator satisfies predictive guarantees in terms of distributional robustness against shifts in a linear class; these guarantees are valid even if the instrumental variable assumptions are violated. If anchor regression and least squares provide the same answer ('anchor stability'), we establish that OLS parameters are invariant under certain distributional changes. Anchor regression is shown empirically to improve replicability and protect against distributional shifts. Show more
Permanent link
https://doi.org/10.3929/ethz-b-000469124Publication status
publishedExternal links
Journal / series
Journal of the Royal Statistical Society Series B: Statistical MethodologyVolume
Pages / Article No.
Publisher
Royal Statistical SocietySubject
causal inference; distributional robustness; replicability; structural equation modellingOrganisational unit
03502 - Bühlmann, Peter L. / Bühlmann, Peter L.
03990 - Meinshausen, Nicolai / Meinshausen, Nicolai
Funding
786461 - Statistics, Prediction and Causality for Large-Scale Data (EC)
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