Generalization Properties of Learning with Random Features
This work addresses the statistical-computational trade-offs in large-scale machine learning, offering a more efficient method for kernel-based models, though it is incremental as it builds on existing random features research.
The paper tackles the problem of reducing computational complexity in kernelized learning by analyzing ridge regression with random features, showing that optimal generalization bounds can be achieved with only O(√n log n) random features instead of O(n), leading to faster learning rates under certain conditions.
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.