Improved analysis of supervised learning in the RKHS with random features: Beyond least squares

Area of Science:

• Machine Learning
• Statistical Learning Theory
• Kernel Methods

Background:

• Kernel-based methods are powerful for supervised learning.
• Random Fourier features offer computational advantages.
• General loss functions present challenges for theoretical analysis.

Purpose of the Study:

• To analyze statistical error bounds and generalization for kernel methods using random Fourier features with general loss functions.
• To establish faster learning rates with fewer features than previously possible for non-least squares losses.
• To address open questions regarding the efficiency of random features.

Main Methods:

• Theoretical analysis of statistical error bounds.
• Investigation of generalization properties for kernel-based supervised learning.
• Utilizing random Fourier features for approximation.

Main Results:

• Established faster learning rates for general Lipschitz loss functions using random Fourier features.
• Achieved optimal rates comparable to least squares loss with significantly fewer features (o(n)).
• Derived a rate of n^{-2ξ/(2ξ+γ)} under source and capacity assumptions.

Conclusions:

• Random Fourier features can achieve optimal learning rates for a broader class of loss functions.
• The number of features required is substantially reduced, improving efficiency.
• This work provides theoretical guarantees for random Fourier features in supervised learning.