Function Estimation via Reconstruction
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This paper introduces an interpolation-based method, called the reconstruction approach, for function estimation in nonparametric models. Based on the fact that interpolation usually has negligible errors compared to statistical estimation, the reconstruction approach uses an interpolator to parameterize the unknown function with its values at finite knots, and then estimates these values by minimizing a regularized empirical risk function. Some popular methods including kernel ridge regression and kernel support vector machines can be viewed as its special cases. It is shown that, the reconstruction idea not only provides different angles to look into existing methods, but also produces new effective experimental design and estimation methods for nonparametric models.
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