Partial transportability for domain generalization

Alexis Bellot, Elias Bareinboim

Keywords: Causality, domain generalization

TL;DR: This paper investigates the problem of domain generalization from the perspective of transportability theory. We propose the task of partial transportability and provide solutions that highlight new contrasts with "invariance learning" methods.

Abstract: Learning prediction models that generalize to related domains is one of the most fundamental challenges in artificial intelligence. There exists a growing literature that argues for learning invariant associations using data from multiple source domains. However, whether invariant predictors generalize to a given target domain depends crucially on the assumed structural changes between domains. Using the perspective of transportability theory, we show that invariance learning, and the settings in which invariant predictors are optimal in terms of worst-case losses, is a special case of a more general partial transportability task. Specifically, the partial transportability task seeks to identify / bound a conditional expectation $\mathbb E_{P_{\pi^*}}[y\mid\mathbf x]$ in an unseen domain $\pi^*$ using knowledge of qualitative changes across domains in the form of causal graphs and data from source domains $\pi^1,\dots,\pi^k$. We show that solutions to this problem have a much wider generalization guarantee that subsumes those of invariance learning and other robust optimization methods that are inspired by causality. For computations in practice, we develop an algorithm that provably provides tight bounds asymptotically in the number of data samples from source domains for any partial transportability problem with discrete observables and illustrate its use on synthetic datasets.

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