A General Scoring Rule for Randomized Kernel Approximation with Application to Canonical Correlation Analysis

Random features has been widely used for kernel approximation in large-scale machine learning. A number of recent studies have explored data-dependent sampling of features, modifying the stochastic oracle from which random features are sampled. While proposed techniques in this realm improve the approximation, their application is limited to a specific learning task. In this paper, we propose a general scoring rule for sampling random features, which can be employed for various applications with some adjustments. We first observe that our method can recover a number of data-dependent sampling methods (e.g., leverage scores and energy-based sampling). Then, we restrict our attention to a ubiquitous problem in statistics and machine learning, namely Canonical Correlation Analysis (CCA). We provide a principled guide for finding the distribution maximizing the canonical correlations, resulting in a novel data-dependent method for sampling features. Numerical experiments verify that our algorithm consistently outperforms other sampling techniques in the CCA task.