Generalization Properties of Learning with Random Features

TL;DR

This paper demonstrates that using a smaller number of random features than previously thought can still achieve optimal generalization bounds in ridge regression, highlighting computational benefits.

Contribution

It establishes new learning bounds with fewer random features and explores conditions for faster rates, advancing understanding of random features in large-scale learning.

Findings

O(1/√n) learning bounds with O(√n log n) features

Faster learning rates possible with more features or specific sampling

Random features can reduce computational complexity while maintaining generalization

Abstract

We study the generalization properties of ridge regression with random features in the statistical learning framework. We show for the first time that $O(1/\sqrt{n})$ learning bounds can be achieved with only $O(\sqrt{n}\log n)$ random features rather than $O({n})$ as suggested by previous results. Further, we prove faster learning rates and show that they might require more random features, unless they are sampled according to a possibly problem dependent distribution. Our results shed light on the statistical computational trade-offs in large scale kernelized learning, showing the potential effectiveness of random features in reducing the computational complexity while keeping optimal generalization properties.