Efficient Interpolation of Density Estimators
This work addresses the challenge of fast and space-efficient querying of kernel density estimators for applications in statistics and machine learning, representing an incremental improvement with a new statistical perspective.
The paper tackles the problem of efficiently evaluating nonparametric density estimators by introducing a piecewise multivariate polynomial interpolation scheme that maintains approximation quality while reducing space and time requirements, achieving computational efficiency without deteriorating statistical performance.
We study the problem of space and time efficient evaluation of a nonparametric estimator that approximates an unknown density. In the regime where consistent estimation is possible, we use a piecewise multivariate polynomial interpolation scheme to give a computationally efficient construction that converts the original estimator to a new estimator that can be queried efficiently and has low space requirements, all without adversely deteriorating the original approximation quality. Our result gives a new statistical perspective on the problem of fast evaluation of kernel density estimators in the presence of underlying smoothness. As a corollary, we give a succinct derivation of a classical result of Kolmogorov---Tikhomirov on the metric entropy of Hölder classes of smooth functions.