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On the Statistical Efficiency of Compositional Nonparametric Prediction
Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics, PMLR 84:1531-1539, 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(klog(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.