Project and Probe: Sample-Efficient Domain Adaptation by Interpolating Orthogonal Features

Conventional approaches to robustness try to learn a model based on causal features. However, identifying maximally robust or causal features may be difficult in some scenarios, and in others, non-causal "shortcut" features may actually be more predictive. We propose a lightweight, sample-efficient approach that learns a diverse set of features and adapts to a target distribution by interpolating these features with a small target dataset. Our approach, Project and Probe (Pro$^2$), first learns a linear projection that maps a pre-trained embedding onto orthogonal directions while being predictive of labels in the source dataset. The goal of this step is to learn a variety of predictive features, so that at least some of them remain useful after distribution shift. Pro$^2$ then learns a linear classifier on top of these projected features using a small target dataset. We theoretically show that Pro$^2$ learns a projection matrix that is optimal for classification in an information-theoretic sense, resulting in better generalization due to a favorable bias-variance tradeoff. Our experiments on four datasets, with multiple distribution shift settings for each, show that Pro$^2$ improves performance by 5-15% when given limited target data compared to prior methods such as standard linear probing.