In multi-class classification problem, the training data and the out-of-sample test data may have different distributions. A method called BCOPS (balanced and conformal optimized prediction sets) constructs a prediction set C(x) as a subset of class labels, possibly empty. It tries to optimize the out-of-sample performance, aiming to include the correct class as often as possible, but also detecting outliers x, for which the method returns no prediction (corresponding to C(x) equal to the empty set).