1. Transfer Learning for Linear Regression: a Statistical Test of Gain
- Author
-
Obst, David, Ghattas, Badih, Cugliari, Jairo, Oppenheim, Georges, Claudel, Sandra, and Goude, Yannig
- Subjects
Mathematics - Statistics Theory ,Computer Science - Machine Learning ,Statistics - Machine Learning - 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 $x$ 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.
- Published
- 2021