Affiliation:
1. Department of Biostatistics Yale University New Haven Connecticut USA
2. Department of Mathematics and Statistics Auburn University Auburn Alabama USA
3. Department of Mathematical Sciences New Jersey Institute of Technology Newark New Jersey USA
Abstract
AbstractWe propose a new approach, called as functional deep neural network (FDNN), for classifying multidimensional functional data. Specifically, a deep neural network is trained based on the principal components of the training data which shall be used to predict the class label of a future data function. Unlike the popular functional discriminant analysis approaches which only work for one‐dimensional functional data, the proposed FDNN approach applies to general non‐Gaussian multidimensional functional data. Moreover, when the log density ratio possesses a locally connected functional modular structure, we show that FDNN achieves minimax optimality. The superiority of our approach is demonstrated through both simulated and real‐world datasets.
Funder
National Science Foundation
Simons Foundation
Subject
Statistics, Probability and Uncertainty,Statistics and Probability
Cited by
4 articles.
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