Reducing labeling costs in supervised learning is a critical issue in many practical machine learning applications. In this paper, we consider positive-confidence (Pconf) classification, the problem of training a binary classifier only from positive data equipped with confidence. Pconf classification can be regarded as a discriminative extension of one-class classification (which is aimed at "describing" the positive class), with ability to tune hyper-parameters for "classifying" positive and negative samples. Pconf classification is also related to positive-unlabeled (PU) classification (which uses hard-labeled positive data and unlabeled data), allowing us to avoid estimating the class priors, which is a critical bottleneck in typical PU classification methods. For the Pconf classification problem, we provide a simple empirical risk minimization framework and give a formulation for linear-in-parameter models that can be implemented easily and computationally efficiently. We also theoretically establish the consistency and generalization error bounds for Pconf classification, and demonstrate the practical usefulness of the proposed method through experiments.

研究如何利用正向数据进行二分类器学习，提出了一种基于正向置信度的分类器，命名为正向置信度（Pconf）分类，提供了一个基于经验风险最小化的框架，理论上证明了其一致性和估计误差界，并通过实验表明了其对训练深度神经网络的有效性。

基于正置信数据的二元分类