# Efficient Interpolation of Density Estimators

arXiv: https://arxiv.org/abs/2011.04922 · HTML: https://mlsanity.com/paper/2011.04922/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Nov 2020.

## Built on by (most cited first, 1 of 1)

- [Fast Approximation of Similarity Graphs with Kernel Density Estimation](https://mlsanity.com/paper/2310.13870/) (2023)

## Abstract (arXiv)

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 H"older classes of smooth functions.