  Given a causal graph representing the data-generating process shared across
different domains/distributions, enforcing sufficient graph-implied conditional
independencies can identify domain-general (non-spurious) feature
representations. For the standard input-output predictive setting, we
categorize the set of graphs considered in the literature into two distinct
groups: (i) those in which the empirical risk minimizer across training domains
gives domain-general representations and (ii) those where it does not. For the
latter case (ii), we propose a novel framework with regularizations, which we
demonstrate are sufficient for identifying domain-general feature
representations without a priori knowledge (or proxies) of the spurious
features. Empirically, our proposed method is effective for both (semi)
synthetic and real-world data, outperforming other state-of-the-art methods in
average and worst-domain transfer accuracy.
