Quasi-Monte Carlo feature maps for shift-invariant Kernels

Haim Avron, Vikas Sindhwani, Jiyan Yang, Michael W. Mahoney

Research output: Contribution to journalArticlepeer-review

56 Scopus citations


We consider the problem of improving the efficiency of randomized Fourier feature maps to accelerate training and testing speed of kernel methods on large data sets. 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.

Original languageEnglish
Pages (from-to)1-38
Number of pages38
JournalJournal of Machine Learning Research
StatePublished - 1 Apr 2016


FundersFunder number
Defense Advanced Research Projects Agency
International Business Machines Corporation
Air Force Research LaboratoryFA8750-12-C-0323


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