On the Statistical Efficiency of Compositional Nonparametric Prediction
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Proceedings of the TwentyFirst International Conference on Artificial Intelligence and Statistics, PMLR 84:15311539, 2018.
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 $Ω(k\log (pq)\log(k!))$. We further propose a greedy algorithm for regression in order to validate our theoretical findings through synthetic experiments.
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