2014/12/29 by Haim Avron, Avron, Haim, Vikas Sindhwani +5 · 3 citations
Mathematics · Medicine · Physics and Astronomy · #Computation (stat.CO) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Mathematical Approximation and Integration #Medical Imaging Techniques and Applications #Nuclear Physics and Applications #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1412.8293
openalex publication_date 2014/12/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the problem of improving the efficiency of randomized Fourier feature maps to accelerate training and testing speed of kernel methods on large datasets. These approximate feature maps arise as Monte Carlo approximations to integral representations of shift-invariant kernel functions (e.g., Gaussian kernel). In this paper, we propose to use Quasi-Monte Carlo (QMC) approximations instead, where the relevant integrands are evaluated on a low-discrepancy sequence of points as opposed to random point sets as in the Monte Carlo approach. We derive a new discrepancy measure called box discrepancy based on theoretical characterizations of the integration error with respect to a given sequence. We then propose to learn QMC sequences adapted to our setting based on explicit box discrepancy minimization. Our theoretical analyses are complemented with empirical results that demonstrate the effectiveness of classical and adaptive QMC techniques for this problem.