Computer Science > Machine Learning
[Submitted on 31 Mar 2024 (v1), last revised 17 Jul 2024 (this version, v2)]
Title:Minimum-Norm Interpolation Under Covariate Shift
View PDF HTML (experimental)Abstract:Transfer learning is a critical part of real-world machine learning deployments and has been extensively studied in experimental works with overparameterized neural networks. However, even in the simplest setting of linear regression a notable gap still exists in the theoretical understanding of transfer learning. In-distribution research on high-dimensional linear regression has led to the identification of a phenomenon known as \textit{benign overfitting}, in which linear interpolators overfit to noisy training labels and yet still generalize well. This behavior occurs under specific conditions on the source covariance matrix and input data dimension. Therefore, it is natural to wonder how such high-dimensional linear models behave under transfer learning. We prove the first non-asymptotic excess risk bounds for benignly-overfit linear interpolators in the transfer learning setting. From our analysis, we propose a taxonomy of \textit{beneficial} and \textit{malignant} covariate shifts based on the degree of overparameterization. We follow our analysis with empirical studies that show these beneficial and malignant covariate shifts for linear interpolators on real image data, and for fully-connected neural networks in settings where the input data dimension is larger than the training sample size.
Submission history
From: Neil Mallinar [view email][v1] Sun, 31 Mar 2024 01:41:57 UTC (254 KB)
[v2] Wed, 17 Jul 2024 08:55:59 UTC (297 KB)
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