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Designing deep neural network classifiers that perform robustly ondistributions differing from the available training data is an active area ofmachine learning research. However, out-of-distribution generalization forregression-the analogous problem for modeling continuous targets-remainsrelatively unexplored. To tackle this problem, we return to first principlesand analyze how the closed-form solution for Ordinary Least Squares (OLS)regression is sensitive to covariate shift. We characterize theout-of-distribution risk of the OLS model in terms of the eigenspectrumdecomposition of the source and target data. We then use this insight topropose a method for adapting the weights of the last layer of a pre-trainedneural regression model to perform better on input data originating from adifferent distribution. We demonstrate how this lightweight spectral adaptationprocedure can improve out-of-distribution performance for synthetic andreal-world datasets.

Out of the Ordinary: Spectrally Adapting Regression for Covariate Shift