论文标题
密度估计器的有效插值
Efficient Interpolation of Density Estimators
论文作者
论文摘要
我们研究了近似于未知密度的非参数估计器的空间和时间效率评估问题。在可能的一致估计的制度中，我们使用分段多元多元插值方案来提供一种计算高效的结构，将原始估计器转换为新的估计器，该估计器可以有效地查询并具有较低的空间需求，而无需不利地降低原始近似质量。我们的结果给出了有关在存在基础平滑度的情况下快速评估内核密度估计器问题的新统计观点。作为推论，我们给出了Kolmogorov的经典结果的简洁推导--- Tikhomirov在Hölder类别的平滑功能类别的度量熵上。
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.
