Positive and Unlabeled (PU) learning is a type of semi-supervised binary classification where the machine learning algorithm differentiates between a set of positive instances (labeled) and a set of both positive and negative instances (unlabeled). PU learning has broad applications in settings where confirmed negatives are unavailable or difficult to obtain, and there is value in discovering positives among the unlabeled (e.g., viable drugs among untested compounds). Most PU learning algorithms make the selected completely at random (SCAR) assumption, namely that positives are selected independently of their features. However, in many real-world applications, such as healthcare, positives are not SCAR (e.g., severe cases are more likely to be diagnosed), leading to a poor estimate of the proportion, $\alpha$, of positives among unlabeled examples and poor model calibration, resulting in an uncertain decision threshold for selecting positives. PU learning algorithms can estimate $\alpha$ or the probability of an individual unlabeled instance being positive or both. We propose two PU learning algorithms to estimate $\alpha$, calculate calibrated probabilities for PU instances, and improve classification metrics: i) PULSCAR (positive unlabeled learning selected completely at random), and ii) PULSNAR (positive unlabeled learning selected not at random). PULSNAR uses a divide-and-conquer approach that creates and solves several SCAR-like sub-problems using PULSCAR. In our experiments, PULSNAR outperformed state-of-the-art approaches on both synthetic and real-world benchmark datasets.

Positive unlabeled learning is a binary classification problem with positive and unlabeled data. It is common in domains where negative labels are costly or impossible to obtain, e.g., medicine and personalized advertising. Most approaches to positive unlabeled learning apply to specific data types (e.g., images, categorical data) and can not generate new positive and negative samples. This work introduces a feature-space distance-based tensor network approach to the positive unlabeled learning problem. The presented method is not domain specific and significantly improves the state-of-the-art results on the MNIST image and 15 categorical/mixed datasets. The trained tensor network model is also a generative model and enables the generation of new positive and negative instances.

Consumer protection agencies are charged with safeguarding the public from hazardous products, but the thousands of products under their jurisdiction make it challenging to identify and respond to consumer complaints quickly. In this paper, we propose a system to mine Amazon.com reviews to identify products that may pose safety or health hazards. Since labeled data for this task are scarce, our approach combines positive unlabeled learning with domain adaptation to train a classifier from consumer complaints submitted to an online government portal. We find that our approach results in an absolute F1 score improvement of 8% over the best competing baseline. Furthermore, when we apply the classifier to Amazon reviews of known recalled products, we identify safety hazard reports prior to the recall date for 45% of the products. This suggests that the system may be able to provide an early warning system to alert consumers to hazardous products before an official recall is announced.