Positiveunlabeled

Positive-unlabeled learning (PU learning) is a subset of semi-supervised machine learning that uses training data consisting of positively labeled instances and unlabeled examples. The unlabeled set may contain both positives and negatives, but negative labels are not explicitly provided.

The objective is to build a classifier that can separate positives from negatives using only the positive examples and the unlabeled data. A central difficulty is that the true class distribution—especially the proportion of positives among the unlabeled examples—is unknown. PU learning often relies on assumptions about how positives are selected for labeling, such as positives being a random sample of all positives (the SCAR assumption).

Methodologically, PU learning falls into two broad families. One consists of two-step approaches that identify a set of reliable negatives within the unlabeled data and then train a conventional classifier. The other consists of direct PU methods that estimate a risk or loss function using only positives and unlabeled data, for example through non-negative risk estimators or unbiased risk estimators; variants include PU-SVM and neural network-based implementations such as nnPU.

A common practical task is estimating the overall proportion of positives in the population (the class prior), which improves calibration and decision thresholds. Evaluation typically requires a labeled test set with true labels; metrics such as AUROC or precision-recall are used, with emphasis on robustness to the assumed selection mechanism.

PU learning has applications in text classification, bioinformatics, fraud detection, and other domains where negative labels are costly or unavailable. Its effectiveness depends on the validity of assumptions about the labeling process and the representativeness of the unlabeled data.