Out of the Ordinary: Spectrally Adapting Regression for Covariate Shift

• URL: http://arxiv.org/abs/2312.17463v1
• Date: Fri, 29 Dec 2023 04:15:58 GMT
• Title: Out of the Ordinary: Spectrally Adapting Regression for Covariate Shift
• Authors: Benjamin Eyre, Elliot Creager, David Madras, Vardan Papyan, Richard Zemel
• Abstract summary: We propose a method 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.
• Score: 12.770658031721435
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 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.

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