On the Statistical Efficiency of Compositional Nonparametric Prediction
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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(pq)+(k!)), and the necessary number of samples is Ω(k (pq)-(k!)). We further propose a greedy algorithm for regression in order to validate our theoretical findings through synthetic experiments.
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