Regularizing towards Causal Invariance: Linear Models with Proxies


We propose a method for learning linear models whose predictive performance is robust to causal interventions on unobserved variables, when noisy proxies of those variables are available. Our approach takes the form of a regularization term that trades off between in-distribution performance and robustness to interventions. Under the assumption of a linear structural causal model, we show that a single proxy can be used to create estimators that are prediction optimal under interventions of bounded strength. This strength depends on the magnitude of the measurement noise in the proxy, which is, in general, not identifiable. In the case of two proxy variables, we propose a modified estimator that is prediction optimal under interventions up to a known strength. We further show how to extend these estimators to scenarios where additional information about the "test time" intervention is available during training. We evaluate our theoretical findings in synthetic experiments and using real data of hourly pollution levels across several cities in China.

arXiv preprint arXiv:2103.02477
Michael Oberst
Michael Oberst
PhD Student

Michael’s research interests include developing learning algorithms for dealing with non-stationarity / dataset shift in predictive modelling, as well as robust learning of treatment policies from observational data.

David Sontag
David Sontag
Associate Professor of EECS

My research focuses on advancing machine learning and artificial intelligence, and using these to transform health care.