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AN ADAPTIVE FACTORIZED NYSTRO\M PRECONDITIONER FOR REGULARIZED KERNEL MATRICES
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DOI：10.1137/23M1565139.png)
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The spectrum of a kernel matrix significantly depends on the parameter values of the kernel function used to define the kernel matrix. This makes it challenging to design a preconditioner for a regularized kernel matrix that is robust across different parameter values. This paper proposes the adaptive factorized Nystrom (AFN) preconditioner. The preconditioner is designed for the case where the rank of the Nystrom approximation is large, i.e., for kernel function parameters that lead to kernel matrices with eigenvalues that decay slowly. AFN deliberately chooses a well-conditioned submatrix to solve with and corrects a Nystr & ouml;m approximation with a factorized sparse approximate matrix inverse. This makes AFN efficient for kernel matrices with large numerical ranks. AFN also adaptively chooses the size of this submatrix to balance accuracy and cost.
Keyword:
kernel matrices
preconditioning
sparse approximate inverse
Nystrom approximation
farthest point sampling
Gaussian process regression
Gaussian process regression
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2.6
论文数:
5.1K
被引数:
1.8W
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