Anchor regression: Heterogeneous data meet causality
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Anchor regression : Heterogeneous data meet causality. / Rothenhäusler, Dominik; Meinshausen, Nicolai; Bühlmann, Peter; Peters, Jonas.
In: Journal of the Royal Statistical Society. Series B: Statistical Methodology, Vol. 83, No. 2, 2021, p. 215 - 246.Research output: Contribution to journal › Journal article › peer-review
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TY - JOUR
T1 - Anchor regression
T2 - Heterogeneous data meet causality
AU - Rothenhäusler, Dominik
AU - Meinshausen, Nicolai
AU - Bühlmann, Peter
AU - Peters, Jonas
PY - 2021
Y1 - 2021
N2 - 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.
AB - 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.
KW - causal inference
KW - distributional robustness
KW - replicability
KW - structural equation modelling
UR - http://www.scopus.com/inward/record.url?scp=85099740900&partnerID=8YFLogxK
U2 - 10.1111/rssb.12398
DO - 10.1111/rssb.12398
M3 - Journal article
AN - SCOPUS:85099740900
VL - 83
SP - 215
EP - 246
JO - Journal of the Royal Statistical Society, Series B (Statistical Methodology)
JF - Journal of the Royal Statistical Society, Series B (Statistical Methodology)
SN - 1369-7412
IS - 2
ER -
ID: 256679165