Keywords: PU learning, Mixture Proportion Estimation
TL;DR: Given only Positive (P) and Unlabeled (U) data, containing both P and Negative (N) samples, we propose new approaches to estimate fraction of P in U and learn P vs N classifier.
Abstract: Given only positive examples and unlabeled examples (from both positive and negative classes), we might hope nevertheless to estimate an accurate positive-versus-negative classifier. Formally, this task is broken down into two subtasks: (i) Mixture Proportion Estimation (MPE)---determining the fraction of positive examples in the unlabeled data; and (ii) PU-learning---given such an estimate, learning the desired positive-versus-negative classifier. Unfortunately, classical methods for both problems break down in high-dimensional settings. Meanwhile, recently proposed heuristics lack theoretical coherence and depend precariously on hyperparameter tuning. In this paper, we propose two simple techniques: Best Bin Estimation (BBE) (for MPE); and Conditional Value Ignoring Risk (CVIR), a simple objective for PU-learning. Both methods dominate previous approaches empirically, and for BBE, we establish formal guarantees that hold whenever we can train a model to cleanly separate out a small subset of positive examples. Our final algorithm (TED)$^n$, alternates between the two procedures, significantly improving both our mixture proportion estimator and classifier
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