On Kernel Regression with Data-Dependent Kernels

• URL: http://arxiv.org/abs/2209.01691v1
• Date: Sun, 4 Sep 2022 20:46:01 GMT
• Title: On Kernel Regression with Data-Dependent Kernels
• Authors: James B. Simon
• Abstract summary: We consider kernel regression in which the kernel may be updated after seeing the training data. Connections to the view of deep neural networks as data-dependent kernel learners are discussed.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The primary hyperparameter in kernel regression (KR) is the choice of kernel. In most theoretical studies of KR, one assumes the kernel is fixed before seeing the training data. Under this assumption, it is known that the optimal kernel is equal to the prior covariance of the target function. In this note, we consider KR in which the kernel may be updated after seeing the training data. We point out that an analogous choice of kernel using the posterior of the target function is optimal in this setting. Connections to the view of deep neural networks as data-dependent kernel learners are discussed.

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