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Kernel matrices appear in machine learning and non-parametric statistics. Given N points in d dimensions and a kernel function that requires O(d) work to evaluate, we present an O(dN N)-work algorithm for the approximate factorization of a regularized kernel matrix, a common computational bottleneck in the training phase of a learning task. With this factorization, solving a linear system with a kernel matrix can be done with O(N N) work. Our algorithm only requires kernel evaluations and doesarXiv:1701.02324v1 fatcat:cmr5qrd6breh5e6wj67vb56tra