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Both this and Nystrom would start with KRR. KRR should put the method to solve the (K+\lambdaI)^-1 system in a method. A subclass would then overload this method and implement the cheaper matrix inversion for Nystrom or incomplete cholesky
This is another important way to approximate kernel methods
See here for a reference implementation (there are also unit tests)
This book also contains a high level description of the algorithm and matlab pseudo-code
This task is closely related to the random fourier features counterpart, #2768
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