Conditional probability estimation based classification with class label missing at random

For binary classification, it is common that class labels of some subjects are missing. Generally, the complete case analysis and the two stage procedure can be used to extend existing full data classification methods to deal with classification with missing class labels. Nevertheless, these two approaches cannot take full advantage of unlabeled subjects. In this paper, binary classification with the class label missing at random (MAR) is considered. Based on the inverse probability weighting (IPW) method and the augmented inverse probability weighting (AIPW) method, two new methods called IPW–CPC and AIPW–CPC are proposed to construct powerful classifiers by estimating the conditional probability in a reproducing kernel Hilbert space (RKHS). Compared with the complete case analysis and the two stage procedure, the proposed IPW–CPC and AIPW–CPC methods can make the best use of unlabeled subjects, which contributes a lot to improving classification accuracy. Theoretically, we show that conditional misclassification rates of the proposed classifiers converge to the Bayes misclassification rate in probability and rates of convergence are also obtained. Finally, simulations and the real data analysis well demonstrate good performances of the proposed IPW–CPC and AIPW–CPC methods in comparison with existing methods.