Classification without labels: Learning from mixed samples in high energy physics

Modern machine learning techniques can be used to construct powerful models for difficult collider physics problems. In many applications, however, these models are trained on imperfect simulations due to a lack of truth-level information in the data, which risks the model learning artifacts of the simulation. In this paper, we introduce the paradigm of classification without labels (CWoLa) in which a classifier is trained to distinguish statistical mixtures of classes, which are common in collider physics. Crucially, neither individual labels nor class proportions are required, yet we prove that the optimal classifier in the CWoLa paradigm is also the optimal classifier in the traditional fully-supervised case where all label information is available. After demonstrating the power of this method in an analytical toy example, we consider a realistic benchmark for collider physics: distinguishing quark- versus gluon-initiated jets using mixed quark/gluon training samples. More generally, CWoLa can be applied to any classification problem where labels or class proportions are unknown or simulations are unreliable, but statistical mixtures of the classes are available.