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Regression is mainly about estimating a function when only a finite number of samples of the function are available. Theories usually care about asymptotic performance as the number of samples tends to infinity. However, Nyquist sampling condition tells that a signal can be fully recovered if the sampling frequency is high enough. Later on, compressed sensing theories give certain conditions to reconstruct sparse signals. So I'm wondering if there are any application of such sampling theories to regression so that we could say when a function could be recovered when a finite number of samples are obtained?

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