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As machine learning algorithms become increasingly sophisticated to exploitsubtle features of the data, they often become more dependent on simulations.This paper presents a new approach called weakly supervised classification inwhich class proportions are the only input into the machine learning algorithm.Using one of the most challenging binary classification tasks in high energyphysics - quark versus gluon tagging - we show that weakly supervisedclassification can match the performance of fully supervised algorithms.Furthermore, by design, the new algorithm is insensitive to any mis-modeling ofdiscriminating features in the data by the simulation. Weakly supervisedclassification is a general procedure that can be applied to a wide variety oflearning problems to boost performance and robustness when detailed simulationsare not reliable or not available.

Weakly Supervised Classification in High Energy Physics