  By inferring latent groups in the training data, recent works introduce
invariant learning to the case where environment annotations are unavailable.
Typically, learning group invariance under a majority/minority split is
empirically shown to be effective in improving out-of-distribution
generalization on many datasets. However, theoretical guarantee for these
methods on learning invariant mechanisms is lacking. In this paper, we reveal
the insufficiency of existing group invariant learning methods in preventing
classifiers from depending on spurious correlations in the training set.
Specifically, we propose two criteria on judging such sufficiency.
Theoretically and empirically, we show that existing methods can violate both
criteria and thus fail in generalizing to spurious correlation shifts.
Motivated by this, we design a new group invariant learning method, which
constructs groups with statistical independence tests, and reweights samples by
group label proportion to meet the criteria. Experiments on both synthetic and
real data demonstrate that the new method significantly outperforms existing
group invariant learning methods in generalizing to spurious correlation
shifts.
