Transfer Learning for Linear Regression: a Statistical Test of Gain
Abstract
Transfer learning, also referred as knowledge transfer, aims at reusing knowledge from a source dataset to a similar target one. While many empirical studies illustrate the benefits of transfer learning, few theoretical results are established especially for regression problems. In this paper a 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.
Cite
@article{arxiv.2102.09504,
title = {Transfer Learning for Linear Regression: a Statistical Test of Gain},
author = {David Obst and Badih Ghattas and Jairo Cugliari and Georges Oppenheim and Sandra Claudel and Yannig Goude},
journal= {arXiv preprint arXiv:2102.09504},
year = {2021}
}