  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.
