AUL is a better optimization metric in PU learning

Traditional binary classification models are trained and evaluated with fully labeled data which is not common in real life. In non-ideal dataset, only a small fraction of positive data are labeled. Training a model from such partially labeled data is named as positive-unlabeled (PU) learning. A naive solution of PU learning is treating unlabeled samples as negative. However, using biased data, the trained model may converge to non-optimal point and its real performance cannot be well estimated. Recent works try to recover the unbiased result by estimating the proportion of positive samples with mixture proportion estimation (MPE) algorithms, but the model performance is still limited and heavy computational cost is introduced (particularly for big datasets). In this work, we theoretically prove that Area Under Lift curve (AUL) is an unbiased metric in PU learning scenario, and the experimental evaluation on 9 datasets shows that the average absolute error of AUL estimation is only 1/6 of AUC estimation. By experiments we also find that, compared with state-of-the-art AUC-optimization algorithm, AULoptimization algorithm can not only significantly save the computational cost, but also improve the model performance by up to 10%.