We address the issue of binary classification from positive and unlabeled data (PU classification) with a selection bias in the positive data. During the observation process, (i) a sample is exposed to a user, (ii) the user then returns the label for the exposed sample, and (iii) we however can only observe the positive samples. Therefore, the positive labels that we observe are a combination of both the exposure and the labeling, which creates a selection bias problem for the observed positive samples. This scenario represents a conceptual framework for many practical applications, such as recommender systems, which we refer to as ``learning from positive, unlabeled, and exposure data'' (PUE classification). To tackle this problem, we initially assume access to data with exposure labels. Then, we propose a method to identify the function of interest using a strong ignorability assumption and develop an ``Automatic Debiased PUE'' (ADPUE) learning method. This algorithm directly debiases the selection bias without requiring intermediate estimates, such as the propensity score, which is necessary for other learning methods. Through experiments, we demonstrate that our approach outperforms traditional PU learning methods on various semi-synthetic datasets.

翻译：我们解决了正例数据存在选择偏差时的正例与无标签数据二分类问题（PU分类）。在观测过程中：（i）样本被暴露给用户，（ii）用户随后对暴露样本返回标签，（iii）但我们只能观测到正例样本。因此，我们观测到的正例标签是曝光与标注共同作用的结果，这导致观测到的正例样本存在选择偏差问题。该场景为推荐系统等许多实际应用提供了概念框架，我们将其称为“从正例、无标签和曝光数据中学习”（PUE分类）。针对该问题，我们首先假设能够获取带有曝光标签的数据。随后，我们基于强可忽略性假设提出了一种识别目标函数的方法，并开发了“自动去偏PUE”（ADPUE）学习方法。该算法无需中间估计量（如其他学习方法所需的倾向得分）即可直接消除选择偏差。实验表明，我们的方法在各种半合成数据集上的表现优于传统PU学习方法。