  In open-set semi-supervised learning (OSSL), we consider unlabeled datasets
that may contain unknown classes. Existing OSSL methods often use the softmax
confidence for classifying data as in-distribution (ID) or out-of-distribution
(OOD). Additionally, many works for OSSL rely on ad-hoc thresholds for ID/OOD
classification, without considering the statistics of the problem. We propose a
new score for ID/OOD classification based on angles in feature space between
data and an ID subspace. Moreover, we propose an approach to estimate the
conditional distributions of scores given ID or OOD data, enabling
probabilistic predictions of data being ID or OOD. These components are put
together in a framework for OSSL, termed \emph{ProSub}, that is experimentally
shown to reach SOTA performance on several benchmark problems. Our code is
available at https://github.com/walline/prosub.
