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Statistical Efficiency of Compositional Nonparametric Prediction

Abstract · Apr 6, 2017 15:43 ·

stat-ml cs-lg

Arxiv Abstract

  • Yixi Xu
  • Jean Honorio
  • Xiao Wang

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 implement our method for regression as a greedy search algorithm, and demonstrate its effectiveness with two synthetic data sets and one real-world experiment.

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