Logistic regression with an auxiliary data source

To achieve good generalization in supervised learning, the training and testing examples are usually required to be drawn from the same source distribution. In this paper we propose a method to relax this requirement in the context of logistic regression. Assuming Dp and Da are two sets of examples drawn from two mismatched distributions, where Da are fully labeled and Dp partially labeled, our objective is to complete the labels of Dp. We introduce an auxiliary variable μ for each example in Da to reflect its mismatch with Dp. Under an appropriate constraint the μ's are estimated as a byproduct, along with the classifier. We also present an active learning approach for selecting the labeled examples in Dp. The proposed algorithm, called "Migratory-Logit" or M-Logit, is demonstrated successfully on simulated as well as real data sets.