Class Prior Estimation from Positive and Unlabeled Data

We consider the problem of learning a classifier using only positive and unlabeled samples. In this setting, it is known that a classifier can be successfully learned if the class prior is available. However, in practice, the class prior is unknown and thus must be estimated from data. In this paper, we propose a new method to estimate the class prior by partially matching the class-conditional density of the positive class to the input density. By performing this partial matching in terms of the Pearson divergence, which we estimate directly without density estimation via lower-bound maximization, we can obtain an analytical estimator of the class prior. We further show that an existing class prior estimation method can also be interpreted as performing partial matching under the Pearson divergence, but in an indirect manner. The superiority of our direct class prior estimation method is illustrated on several benchmark datasets.