Scalable Learning in Reproducing Kernel Kre?n Spaces

Abstract

We provide the first mathematically complete derivation of the Nyström method for low-rank approximation of indefinite kernels and propose an efficient method for finding an approximate eigen-decomposition of such kernel matrices. Building on this result, we devise highly scalable methods for learning in reproducing kernel Kre˘ ın spaces. The devised approaches provide a principled and theoretically well-founded means to tackle large scale learning problems with indefinite kernels. The main motivation for our work comes from problems with structured representations (e.g., graphs, strings, time-series), where it is relatively easy to devise a pairwise (dis)similarity function based on intuition and/or knowledge of domain experts. Such functions are typically not positive definite and it is often well beyond the expertise of practitioners to verify this condition. The effectiveness of the devised approaches is evaluated empirically using indefinite kernels defined on structured and vectorial data representations.

Citation

Oglic, D., & Gärtner, T. (2019). Scalable Learning in Reproducing Kernel Kreĭn Spaces.

• Conference Name: 36th International Conference on Machine Learning (ICML 2019)
• Start Date: Jun 9, 2019
• End Date: Jun 15, 2019
• Acceptance Date: Apr 22, 2019
• Online Publication Date: Jun 13, 2019
• Publication Date: Jun 13, 2019
• Deposit Date: Jun 24, 2019
• Publicly Available Date: Jun 24, 2019
• Volume: 97
• Pages: 4912-4921
• Series Title: Proceedings of Machine Learning Research
• Series ISSN: 2640-3498
• Public URL: https://nottingham-repository.worktribe.com/output/2223107
• Publisher URL: http://proceedings.mlr.press/v97/oglic19a.html