Jul 12, 2020
Random Features (RF) models are used as efficient parametric approximations of kernel methods. We investigate, by means of random matrix theory, the connection between Gaussian RF models and Kernel Ridge Regression (KRR). For a Gaussian RF model with P features, N data points, and a ridge λ, we show that the average (i.e. expected) RF predictor is close to a KRR predictor with an effective ridge λ̃. We show that λ̃ > λ and λ̃↘λ monotonically as P grows, thus revealing the implicit regularization effect of finite RF sampling. We then compare the risk (i.e. test error) of the λ̃-KRR predictor with the average risk of the λ-RF predictor and obtain a precise and explicit bound on their difference. Finally, we empirically find an extremely good agreement between the test errors of the average λ-RF predictor and λ̃-KRR predictor.
The International Conference on Machine Learning (ICML) is the premier gathering of professionals dedicated to the advancement of the branch of artificial intelligence known as machine learning. ICML is globally renowned for presenting and publishing cutting-edge research on all aspects of machine learning used in closely related areas like artificial intelligence, statistics and data science, as well as important application areas such as machine vision, computational biology, speech recognition, and robotics. ICML is one of the fastest growing artificial intelligence conferences in the world. Participants at ICML span a wide range of backgrounds, from academic and industrial researchers, to entrepreneurs and engineers, to graduate students and postdocs.
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