Random Features for Kernel Approximation: A Survey on Algorithms, Theory, and Beyond.

Area of Science:

• Machine Learning
• Computational Statistics
• Kernel Methods

Background:

• Random features are a key technique for accelerating kernel methods in large-scale machine learning problems.
• The field has seen rapid growth, necessitating a consolidated overview of algorithms and theory.
• Related work has received significant recognition, including prestigious awards.

Purpose of the Study:

• To systematically review random feature methods developed over the past decade.
• To explain the connections between various algorithms and theoretical findings.
• To serve as an introduction and practical guide for researchers and practitioners.

Main Methods:

• Summarizing representative random feature algorithms based on sampling, learning procedures, and variance reduction.
• Reviewing theoretical results on the number of random features required for approximation quality.
• Evaluating popular algorithms on benchmark datasets for classification performance.
• Discussing the relationship between random features and deep neural networks.

Main Results:

• Categorization of random feature algorithms by their characteristics and data exploitation.
• Analysis of theoretical bounds for approximation quality and risk.
• Empirical evaluation demonstrating the performance of various random feature methods.
• Exploration of the links between random features and the analysis of deep neural networks.

Conclusions:

• The survey offers a structured overview of random features, bridging theory and practice.
• It highlights the utility of random features in understanding and analyzing deep learning models.
• The work aims to stimulate further research and discussion on open problems in the field.