Fast DPP Sampling for Nyström with Application to Kernel Methods
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Jegelka_Fast DPP.pdf
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696.8 KB
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Author(s)
Li, Chengtao
Jegelka, Stefanie Sabrina
Sra, Suvrit
Date Issued
June 2016
Journal
International Conference on Machine Learning
Publisher
Proceedings of Machine Learning Research
Citation
Li, Chengtao, Stefanie Jegelka, and Suvrit Sra. "Fast Dpp Sampling for Nyström with Application to Kernel Methods." International Conference on Machine Learning, 20-22 June, 2016, New York, New York, Proceedings of Machine Learning Research, 2016.
Version
Original manuscript
Abstract
The Nyström method has long been popular for scaling up kernel methods. Its theoretical guarantees and empirical performance rely critically on the quality of the landmarks selected. We study landmark selection for Nyström using Determinantal Point Processes (Dpps), discrete probability models that allow tractable generation of diverse samples. We prove that landmarks
selected via Dpps guarantee bounds on approximation errors; subsequently, we analyze implications for kernel ridge regression. Contrary to prior reservations due to cubic complexity of Dpp sampling, we show that (under certain conditions) Markov chain Dpp sampling requires only linear time in the size of the data. We present several empirical results that support our theoretical analysis, and demonstrate the superior performance of Dpp-based landmark selection compared with existing approaches
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
http://proceedings.mlr.press/v48/
