Geometry-Aware Instrumental Variable Regression
This work addresses robustness issues in instrumental variable regression for applications dealing with corrupted or adversarial data, representing an incremental improvement over existing methods.
The paper tackles the problem of instrumental variable regression in the presence of corrupted or adversarial data by proposing the Sinkhorn Method of Moments, an optimal transport-based estimator that incorporates data geometry. The result is a method that performs comparably to existing estimators in standard settings but shows improved robustness against data corruption and attacks.
Instrumental variable (IV) regression can be approached through its formulation in terms of conditional moment restrictions (CMR). Building on variants of the generalized method of moments, most CMR estimators are implicitly based on approximating the population data distribution via reweightings of the empirical sample. While for large sample sizes, in the independent identically distributed (IID) setting, reweightings can provide sufficient flexibility, they might fail to capture the relevant information in presence of corrupted data or data prone to adversarial attacks. To address these shortcomings, we propose the Sinkhorn Method of Moments, an optimal transport-based IV estimator that takes into account the geometry of the data manifold through data-derivative information. We provide a simple plug-and-play implementation of our method that performs on par with related estimators in standard settings but improves robustness against data corruption and adversarial attacks.