  Modern machine learning models may be susceptible to learning spurious
correlations that hold on average but not for the atypical group of samples. To
address the problem, previous approaches minimize the empirical worst-group
risk. Despite the promise, they often assume that each sample belongs to one
and only one group, which does not allow expressing the uncertainty in group
labeling. In this paper, we propose a novel framework PG-DRO, which explores
the idea of probabilistic group membership for distributionally robust
optimization. Key to our framework, we consider soft group membership instead
of hard group annotations. The group probabilities can be flexibly generated
using either supervised learning or zero-shot approaches. Our framework
accommodates samples with group membership ambiguity, offering stronger
flexibility and generality than the prior art. We comprehensively evaluate
PG-DRO on both image classification and natural language processing benchmarks,
establishing superior performance
