L_2-norm sampling discretization and recovery of functions from RKHS with finite trace
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We provide a spectral norm concentration inequality for infinite random matrices with independent rows. This complements earlier results by Mendelson, Pajor, Oliveira and Rauhut. As an application we study L_2-norm sampling discretization and recovery of functions in RKHS on D ⊂ℝ^d based on random function samples, where we only assume the finite trace of the kernel. We provide several concrete estimates with precise constants for the corresponding worst-case errors. The fail probability is controlled and decays polynomially in n, the number of samples. In general, our analysis does not need any additional assumptions and also includes the case of kernels on non-compact domains. However, under the mild additional assumption of separability we observe improved rates of convergence.
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