On the Statistical Efficiency of Compositional Nonparametric Prediction
Abstract
In this paper, we propose a compositional nonparametric method in which a model is expressed as a labeled binary tree of $2k+1$ nodes, where each node is either a summation, a multiplication, or the application of one of the $q$ basis functions to one of the $p$ covariates. We show that in order to recover a labeled binary tree from a given dataset, the sufficient number of samples is $O(k\log(pq)+\log(k!))$, and the necessary number of samples is $\Omega(k\log (pq)-\log(k!))$. We further propose a greedy algorithm for regression in order to validate our theoretical findings through synthetic experiments.
Cite
Text
Xu et al. "On the Statistical Efficiency of Compositional Nonparametric Prediction." International Conference on Artificial Intelligence and Statistics, 2018.Markdown
[Xu et al. "On the Statistical Efficiency of Compositional Nonparametric Prediction." International Conference on Artificial Intelligence and Statistics, 2018.](https://mlanthology.org/aistats/2018/xu2018aistats-statistical/)BibTeX
@inproceedings{xu2018aistats-statistical,
title = {{On the Statistical Efficiency of Compositional Nonparametric Prediction}},
author = {Xu, Yixi and Honorio, Jean and Wang, Xiao},
booktitle = {International Conference on Artificial Intelligence and Statistics},
year = {2018},
pages = {1531-1539},
url = {https://mlanthology.org/aistats/2018/xu2018aistats-statistical/}
}