High-Dimensional Kernel Methods under Covariate Shift: Data-Dependent Implicit Regularization

• URL: http://arxiv.org/abs/2406.03171v1
• Date: Wed, 5 Jun 2024 12:03:27 GMT
• Title: High-Dimensional Kernel Methods under Covariate Shift: Data-Dependent Implicit Regularization
• Authors: Yihang Chen, Fanghui Liu, Taiji Suzuki, Volkan Cevher,
• Abstract summary: This paper studies kernel ridge regression in high dimensions under covariate shifts. By a bias-variance decomposition, we theoretically demonstrate that the re-weighting strategy allows for decreasing the variance. For bias, we analyze the regularization of the arbitrary or well-chosen scale, showing that the bias can behave very differently under different regularization scales.
• Score: 83.06112052443233
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This paper studies kernel ridge regression in high dimensions under covariate shifts and analyzes the role of importance re-weighting. We first derive the asymptotic expansion of high dimensional kernels under covariate shifts. By a bias-variance decomposition, we theoretically demonstrate that the re-weighting strategy allows for decreasing the variance. For bias, we analyze the regularization of the arbitrary or well-chosen scale, showing that the bias can behave very differently under different regularization scales. In our analysis, the bias and variance can be characterized by the spectral decay of a data-dependent regularized kernel: the original kernel matrix associated with an additional re-weighting matrix, and thus the re-weighting strategy can be regarded as a data-dependent regularization for better understanding. Besides, our analysis provides asymptotic expansion of kernel functions/vectors under covariate shift, which has its own interest.

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