Prediction Interval Transfer Learning for Linear Regression Using an Empirical Bayes Approach

Current literature on transfer learning has been focused on improving the predictive performance corresponding to a small dataset by transferring information to it from a larger but possibly biassed dataset. However, the transfer learning methods currently available do not allow the computation of prediction intervals, and hence, one has to rely on using either the small dataset alone or combining it with the possibly biassed dataset to obtain prediction intervals using traditional linear regression methods. In this article, we propose an Empirical Bayes approach for Prediction Interval Transfer Learning (EB-PITL), to compute prediction intervals for transfer learning in linear regression tasks. We have proved that the Gibbs sampler associated with EB-PITL is geometrically ergodic, so EB-PITL can also quantify the Monte Carlo uncertainty associated with its predicted value. The efficiency of EB-PITL against currently available methods is demonstrated using simulation studies and by analysing the Tetouan City power consumption dataset.