Ridgeless Regression with Random Features

Ridgeless Regression with Random Features

Jian Li, Yong Liu, Yingying Zhang

Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence
Main Track. Pages 3208-3214. https://doi.org/10.24963/ijcai.2022/445

Recent theoretical studies illustrated that kernel ridgeless regression can guarantee good generalization ability without an explicit regularization. In this paper, we investigate the statistical properties of ridgeless regression with random features and stochastic gradient descent. We explore the effect of factors in the stochastic gradient and random features, respectively. Specifically, random features error exhibits the double-descent curve. Motivated by the theoretical findings, we propose a tunable kernel algorithm that optimizes the spectral density of kernel during training. Our work bridges the interpolation theory and practical algorithm.
Keywords:
Machine Learning: Learning Theory
Machine Learning: Kernel Methods