Mixture Proportion Estimation and PU Learning: A Modern Approach
This addresses the challenge of semi-supervised learning in high-dimensional settings where classical methods fail, offering a more robust solution for applications like medical diagnosis or spam filtering.
The paper tackles the problem of learning a classifier from only positive and unlabeled data, proposing two techniques: Best Bin Estimation for mixture proportion estimation and Conditional Value Ignoring Risk for PU-learning, which empirically dominate previous approaches and include formal guarantees for BBE.
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