Approximate Kernel PCA Using Random Features: Computational vs. Statistical Trade-off

Understand

Kernel methods are powerful learning methodologies that allow to perform non-linear data analysis.

• Despite their popularity, they suffer from poor scalability in big data scenarios.
• Various approximation methods, including random feature approximation, have been proposed to alleviate the problem.
• However, the statistical consistency of most of these approximate kernel methods is not well understood except for kernel ridge regression wherein it has been shown that the random feature approximation is not only computationally efficient but also statistically consistent with a minimax optimal rate of convergence.