Mixture Proportion Estimation and PU Learning: A Modern Approach
Mixture Proportion Estimation and PU Learning: A Modern Approach
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发表时间：
2021-11
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通讯作者：
S. Garg;Yifan Wu;Alexander J. Smola;Sivaraman Balakrishnan;Zachary Chase Lipton
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作者：
S. Garg;Yifan Wu;Alexander J. Smola;Sivaraman Balakrishnan;Zachary Chase Lipton
只给出肯定的例子和未标记的例子（来自肯定类和否定类），我们仍然希望估计出一个准确的肯定与否定分类器。从形式上讲，这个任务被分解为两个子任务：（i）混合比例估计（MPE）-确定未标记数据中阳性样本的比例;以及（ii）PU学习-给定这样的估计，学习所需的阳性与阴性分类器。不幸的是，这两个问题的经典方法在高维环境中崩溃。与此同时，最近提出的算法缺乏理论上的一致性，并且不稳定地依赖于超参数调整。在本文中，我们提出了两种简单的技术：最佳箱估计（BBE）（用于MPE）;和条件值忽略风险（CVIR），这是PU学习的一个简单目标。这两种方法在经验上都主导了以前的方法，对于BBE，我们建立了正式的保证，只要我们可以训练模型，就可以干净地分离出一小部分正面示例。我们的最终算法（TED）$^n$，在两个过程之间交替，显着改善了我们的混合比例估计器和分类器
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