Migratory Logistic Regression for Learning Concept Drift Between Two Data Sets With Application to UXO Sensing

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 D ^p and D ^a are two sets of examples drawn from two different distributions T and A (called concepts, borrowing a term from psychology), where D ^a are fully labeled and D ^p partially labeled, our objective is to complete the labels of D ^p. We introduce an auxiliary variable mu for each example in D ^a to reflect its mismatch with D ^p. Under an appropriate constraint the mus are estimated as a byproduct, along with the classifier. We also present an active learning approach for selecting the labeled examples in D ^p. The proposed algorithm, called migratory logistic regression, is demonstrated successfully on simulated data as well as on real measured data of interest for unexploded ordnance cleanup.