We tackle the Few-Shot Open-Set Recognition (FSOSR) problem, i.e. classifying instances among a set of classes for which we only have a few labeled samples, while simultaneously detecting instances that do not belong to any known class. We explore the popular transductive setting, which leverages the unlabelled query instances at inference. Motivated by the observation that existing transductive methods perform poorly in open-set scenarios, we propose a generalization of the maximum likelihood principle, in which latent scores down-weighing the influence of potential outliers are introduced alongside the usual parametric model. Our formulation embeds supervision constraints from the support set and additional penalties discouraging overconfident predictions on the query set. We proceed with a block-coordinate descent, with the latent scores and parametric model co-optimized alternately, thereby benefiting from each other. We call our resulting formulation \textit{Open-Set Likelihood Optimization} (OSLO). OSLO is interpretable and fully modular; it can be applied on top of any pre-trained model seamlessly. Through extensive experiments, we show that our method surpasses existing inductive and transductive methods on both aspects of open-set recognition, namely inlier classification and outlier detection.
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