JUST INTERPOLATE: KERNEL RIDGELESS REGRESSION CAN GENERALIZE

• 成果类型: Article
• 署名作者: Liang, Tengyuan; Rakhlin, Alexander
• 署名单位: University of Chicago; Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT)
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/19-AOS1849
• 发表日期: 2020
• 页码: 1329-1347
• 关键词: rates

摘要

In the absence of explicit regularization, Kernel Ridgeless Regression with nonlinear kernels has the potential to fit the training data perfectly. It has been observed empirically, however, that such interpolated solutions can still generalize well on test data. We isolate a phenomenon of implicit regularization for minimum-norm interpolated solutions which is due to a combination of high dimensionality of the input data, curvature of the kernel function and favorable geometric properties of the data such as an eigenvalue decay of the empirical covariance and kernel matrices. In addition to deriving a data-dependent upper bound on the out-of-sample error, we present experimental evidence suggesting that the phenomenon occurs in the MNIST dataset.