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arXiv · 2102.09504

Transfer Learning for Linear Regression: a Statistical Test of Gain

David Obst·Badih Ghattas·Jairo Cugliari·Georges Oppenheim·Sandra Claudel·Yannig Goude
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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.

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BibTeXRIS

David Obst, Badih Ghattas, Jairo Cugliari, Georges Oppenheim, Sandra Claudel, Yannig Goude. 2021-02-18. Transfer Learning for Linear Regression: a Statistical Test of Gain. https://arxiv.org/abs/2102.09504

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