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Improved linear regression prediction by transfer learning

Author

Listed:
  • Obst, David
  • Ghattas, Badih
  • Claudel, Sandra
  • Cugliari, Jairo
  • Goude, Yannig
  • Oppenheim, Georges

Abstract

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.

Suggested Citation

  • Obst, David & Ghattas, Badih & Claudel, Sandra & Cugliari, Jairo & Goude, Yannig & Oppenheim, Georges, 2022. "Improved linear regression prediction by transfer learning," Computational Statistics & Data Analysis, Elsevier, vol. 174(C).
    • Handle: RePEc:eee:csdana:v:174:y:2022:i:c:s0167947322000792
    DOI: 10.1016/j.csda.2022.107499
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    References listed on IDEAS

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    1. Long Cai & Jie Gu & Jinghuan Ma & Zhijian Jin, 2019. "Probabilistic Wind Power Forecasting Approach via Instance-Based Transfer Learning Embedded Gradient Boosting Decision Trees," Energies, MDPI, vol. 12(1), pages 1-19, January.
    2. Hong, Tao & Pinson, Pierre & Fan, Shu, 2014. "Global Energy Forecasting Competition 2012," International Journal of Forecasting, Elsevier, vol. 30(2), pages 357-363.
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