Improved linear regression prediction by transfer learning

Transfer learning, also referred as knowledge transfer, aims at reusing knowledge from a source dataset to a similar target one. While several studies address the problem of what to transfer, the very important question of when to answer remains mostly unanswered, especially from a theoretical point-of-view for regression problems. A new theoretical framework for the problem of parameter transfer for the linear model is proposed. It is shown that the quality of transfer for a new input vector depends on its representation in an eigenbasis involving the parameters of the problem. Furthermore, a statistical test is constructed to predict whether a fine-tuned model has a lower prediction quadratic risk than the base target model for an unobserved sample. Efficiency of the test is illustrated on synthetic data as well as real electricity consumption data.(C) 2022 Elsevier B.V. All rights reserved.