Transfer Learning for Linear Regression: a Statistical Test of Gain

• URL: http://arxiv.org/abs/2102.09504v1
• Date: Thu, 18 Feb 2021 17:46:26 GMT
• Title: Transfer Learning for Linear Regression: a Statistical Test of Gain
• Authors: David Obst and Badih Ghattas and Jairo Cugliari and Georges Oppenheim and Sandra Claudel and Yannig Goude
• Abstract summary: Transfer learning aims at reusing knowledge from a source dataset to a similar target one. It is shown that the quality of transfer for a new input vector $x$ depends on its representation in an eigenbasis. A statistical test is constructed to predict whether a fine-tuned model has a lower prediction quadratic risk than the base target model.
• Score: 2.1550839871882017
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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