Fast DPP Sampling for Nyström with Application to Kernel Methods
Author(s)Li, Chengtao; Jegelka, Stefanie Sabrina; Sra, Suvrit
MetadataShow full item record
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
DepartmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
International Conference on Machine Learning
Proceedings of Machine Learning Research
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.