Near-Linear Time Local Polynomial Nonparametric Estimation with Box Kernels
Computation
2020-09-01 v2 Data Structures and Algorithms
Machine Learning
Machine Learning
Abstract
Local polynomial regression (Fan and Gijbels 1996) is an important class of methods for nonparametric density estimation and regression problems. However, straightforward implementation of local polynomial regression has quadratic time complexity which hinders its applicability in large-scale data analysis. In this paper, we significantly accelerate the computation of local polynomial estimates by novel applications of multi-dimensional binary indexed trees (Fenwick 1994). Both time and space complexity of our proposed algorithm is nearly linear in the number of input data points. Simulation results confirm the efficiency and effectiveness of our proposed approach.
Cite
@article{arxiv.1802.09578,
title = {Near-Linear Time Local Polynomial Nonparametric Estimation with Box Kernels},
author = {Yining Wang and Yi Wu and Simon S. Du},
journal= {arXiv preprint arXiv:1802.09578},
year = {2020}
}
Comments
Accepted to INFORMS Journal on Computing