  We propose Okapi, a simple, efficient, and general method for robust
semi-supervised learning based on online statistical matching. Our method uses
a nearest-neighbours-based matching procedure to generate cross-domain views
for a consistency loss, while eliminating statistical outliers. In order to
perform the online matching in a runtime- and memory-efficient way, we draw
upon the self-supervised literature and combine a memory bank with a
slow-moving momentum encoder. The consistency loss is applied within the
feature space, rather than on the predictive distribution, making the method
agnostic to both the modality and the task in question. We experiment on the
WILDS 2.0 datasets Sagawa et al., which significantly expands the range of
modalities, applications, and shifts available for studying and benchmarking
real-world unsupervised adaptation. Contrary to Sagawa et al., we show that it
is in fact possible to leverage additional unlabelled data to improve upon
empirical risk minimisation (ERM) results with the right method. Our method
outperforms the baseline methods in terms of out-of-distribution (OOD)
generalisation on the iWildCam (a multi-class classification task) and
PovertyMap (a regression task) image datasets as well as the CivilComments (a
binary classification task) text dataset. Furthermore, from a qualitative
perspective, we show the matches obtained from the learned encoder are strongly
semantically related. Code for our paper is publicly available at
https://github.com/wearepal/okapi/.
