Out of the Ordinary: Spectrally Adapting Regression for Covariate Shift

Benjamin Eyre, Elliot Creager, David Madras, Vardan Papyan, Richard Zemel
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:12701-12722, 2024.

Abstract

Designing deep neural network classifiers that perform robustly on distributions differing from the available training data is an active area of machine learning research. However, out-of-distribution generalization for regression—the analogous problem for modeling continuous targets—remains relatively unexplored. To tackle this problem, we return to first principles and analyze how the closed-form solution for Ordinary Least Squares (OLS) regression is sensitive to covariate shift. We characterize the out-of-distribution risk of the OLS model in terms of the eigenspectrum decomposition of the source and target data. We then use this insight to propose a method called Spectral Adapted Regressor (SpAR) for adapting the weights of the last layer of a pre-trained neural regression model to perform better on input data originating from a different distribution. We demonstrate how this lightweight spectral adaptation procedure can improve out-of-distribution performance for synthetic and real-world datasets.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-eyre24a, title = {Out of the Ordinary: Spectrally Adapting Regression for Covariate Shift}, author = {Eyre, Benjamin and Creager, Elliot and Madras, David and Papyan, Vardan and Zemel, Richard}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {12701--12722}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/eyre24a/eyre24a.pdf}, url = {https://proceedings.mlr.press/v235/eyre24a.html}, abstract = {Designing deep neural network classifiers that perform robustly on distributions differing from the available training data is an active area of machine learning research. However, out-of-distribution generalization for regression—the analogous problem for modeling continuous targets—remains relatively unexplored. To tackle this problem, we return to first principles and analyze how the closed-form solution for Ordinary Least Squares (OLS) regression is sensitive to covariate shift. We characterize the out-of-distribution risk of the OLS model in terms of the eigenspectrum decomposition of the source and target data. We then use this insight to propose a method called Spectral Adapted Regressor (SpAR) for adapting the weights of the last layer of a pre-trained neural regression model to perform better on input data originating from a different distribution. We demonstrate how this lightweight spectral adaptation procedure can improve out-of-distribution performance for synthetic and real-world datasets.} }
Endnote
%0 Conference Paper %T Out of the Ordinary: Spectrally Adapting Regression for Covariate Shift %A Benjamin Eyre %A Elliot Creager %A David Madras %A Vardan Papyan %A Richard Zemel %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-eyre24a %I PMLR %P 12701--12722 %U https://proceedings.mlr.press/v235/eyre24a.html %V 235 %X Designing deep neural network classifiers that perform robustly on distributions differing from the available training data is an active area of machine learning research. However, out-of-distribution generalization for regression—the analogous problem for modeling continuous targets—remains relatively unexplored. To tackle this problem, we return to first principles and analyze how the closed-form solution for Ordinary Least Squares (OLS) regression is sensitive to covariate shift. We characterize the out-of-distribution risk of the OLS model in terms of the eigenspectrum decomposition of the source and target data. We then use this insight to propose a method called Spectral Adapted Regressor (SpAR) for adapting the weights of the last layer of a pre-trained neural regression model to perform better on input data originating from a different distribution. We demonstrate how this lightweight spectral adaptation procedure can improve out-of-distribution performance for synthetic and real-world datasets.
APA
Eyre, B., Creager, E., Madras, D., Papyan, V. & Zemel, R.. (2024). Out of the Ordinary: Spectrally Adapting Regression for Covariate Shift. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:12701-12722 Available from https://proceedings.mlr.press/v235/eyre24a.html.

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