Ridgeless Regression with Random Features

• URL: http://arxiv.org/abs/2205.00477v1
• Date: Sun, 1 May 2022 14:25:08 GMT
• Title: Ridgeless Regression with Random Features
• Authors: Jian Li, Yong Liu, Yingying Zhang
• Abstract summary: We investigate the statistical properties of ridgeless regression with random features and gradient descent. We propose a tunable kernel algorithm that optimize the spectral density of kernel during training.
• Score: 23.41536146432726
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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