A linear adjustment based approach to posterior drift in transfer learning

We present a new model and methods for the posterior drift problem where the regression function in the target domain is modeled as a linear adjustment (on an appropriate scale) of that in the source domain, an idea that inherits the simplicity and the usefulness of generalized linear models and accelerated failure time models from the classical statistics literature, and study the theoretical properties of our proposed estimator in the binary classification problem. Our approach is shown to be flexible and applicable in a variety of statistical settings, and can be adopted to transfer learning problems in various domains including epidemiology, genetics and biomedicine. As a concrete application, we illustrate the power of our approach through mortality prediction for British Asians by borrowing strength from similar data from the larger pool of British Caucasians, using the UK Biobank data.