(Machine) learning to do more with less

Determining the best method for training a machine learning algorithm is critical to maximizing its ability to classify data. In this paper, we compare the standard fully supervised approach (which relies on knowledge of event-by-event truth-level labels) with a recent proposal that instead utilizes class ratios as the only discriminating information provided during training. This so-called weakly supervised technique has access to less information than the fully supervised method and yet is still able to yield impressive discriminating power. In addition, weak supervision seems particularly well suited to particle physics since quantum mechanics is incompatible with the notion of mapping an individual event onto any single Feynman diagram. We examine the technique in detail both analytically and numerically with a focus on the robustness to issues of mischaracterizing the training samples. Weakly supervised networks turn out to be remarkably insensitive to a class of systematic mismodeling. Furthermore, we demonstrate that the event level outputs for weakly versus fully supervised networks are probing different kinematics, even though the numerical quality metrics are essentially identical. This implies that it should be possible to improve the overall classification ability by combining the output from the two types of networks. For concreteness, we apply this technology to a signature of beyond the Standard Model physics to demonstrate that all these impressive features continue to hold in a scenario of relevance to the LHC. Example code is provided on GitHub.