Title: Dirichlet Wrapper to Quantify Classification Uncertainty in Black-Box Systems. Abstract: Nowadays, machine learning models are becoming a utility in many sectors. AI companies deliver pre-trained encapsulated models as application programming interfaces (APIs) that developers can combine with third party components, their models, and proprietary data, to create complex data products. This complexity and the lack of control and knowledge of the internals of these external components might cause unavoidable effects, such as lack of transparency, difficulty in auditability, and the emergence of uncontrolled potential risks. These issues are especially critical when practitioners use these components as black-boxes in new datasets. In order to provide actionable insights in this type of scenarios, in this work we propose the use of a wrapping deep learning model to enrich the output of a classification black-box with a measure of uncertainty. Given a black-box classifier, we propose a probabilistic neural network that works in parallel to the black-box and uses a Dirichlet layer as the fusion layer with the black-box.  This Dirichlet layer yields a distribution on top of the multinomial output parameters of the classifier and enables the estimation of aleatoric uncertainty for any data sample.  
Based on the resulting uncertainty measure, we advocate for a rejection system that selects the more confident predictions, discarding those more uncertain, leading to an improvement in the trustability of the resulting system. We showcase the proposed technique and methodology in two practical scenarios, one for NLP and another for computer vision, where a simulated API based is applied to different domains. Results demonstrate the effectiveness of the uncertainty computed by the wrapper and its high correlation to wrong predictions and misclassifications.