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.

We present PROSUB: PROgressive SUBsampling, a deep learning based, automated methodology that subsamples an oversampled data set (e.g. multi-channeled 3D images) with minimal loss of information. We build upon a recent dual-network approach that won the MICCAI MUlti-DIffusion (MUDI) quantitative MRI measurement sampling-reconstruction challenge, but suffers from deep learning training instability, by subsampling with a hard decision boundary. PROSUB uses the paradigm of recursive feature elimination (RFE) and progressively subsamples measurements during deep learning training, improving optimization stability. PROSUB also integrates a neural architecture search (NAS) paradigm, allowing the network architecture hyperparameters to respond to the subsampling process. We show PROSUB outperforms the winner of the MUDI MICCAI challenge, producing large improvements >18% MSE on the MUDI challenge sub-tasks and qualitative improvements on downstream processes useful for clinical applications. We also show the benefits of incorporating NAS and analyze the effect of PROSUB's components. As our method generalizes to other problems beyond MRI measurement selection-reconstruction, our code is https://github.com/sbb-gh/PROSUB