Many Machine Learning algorithms aiming at classifying signals/images X among a number of discrete labels Y involve training instances, from which the predictor P Y |X is extracted according to the data distribution P X|Y. This predictor is later used to predict the appropriate label for other instances of X that are hence assumed to be drawn from the same distribution. This is a fundamental requirement for many real-world applications, therefore it is of great importance to monitor the reliability of the classification provided by the algorithm based on the learned distributions, when the test set statistics differ from the training set ones. This paper makes a step in that direction by proposing a Black Box Shift Detector of the data evolution (covariate shift). 'Black Box' here means that it does not require any knowledge of the predictor's architecture. Experiments demonstrate accurate detection on different high-dimensional datasets of natural images.