  We propose a Target Conditioned Representation Independence (TCRI) objective
for domain generalization. TCRI addresses the limitations of existing domain
generalization methods due to incomplete constraints. Specifically, TCRI
implements regularizers motivated by conditional independence constraints that
are sufficient to strictly learn complete sets of invariant mechanisms, which
we show are necessary and sufficient for domain generalization. Empirically, we
show that TCRI is effective on both synthetic and real-world data. TCRI is
competitive with baselines in average accuracy while outperforming them in
worst-domain accuracy, indicating desired cross-domain stability.
