A0730
Title: Nonparametric function-on-scalar regression with deep learning
Authors: Kazunori Takeshita - Osaka university (Japan) [presenting]
Yoshikazu Terada - Osaka University; RIKEN (Japan)
Abstract: Nonlinear function-on-scalar (FOS) regression is considered using neural networks, where the predictor variables are scalar, and the response variables are functional data. Previous research proposed methods based on the approximation theory of neural networks. The advantage of the method is that it can be applied without imposing specific assumptions (such as additive models) on the true function, even when the dimensions of the predictor variables are relatively large. However, since the estimator is represented through basis functions, it lacks the adaptability that is known as an advantage of deep learning. To overcome this shortcoming, a new adaptive estimator is proposed using deep neural networks and the theoretical properties of the proposed method are shown. More precisely, the anisotropic Besov space is considered a model of true function. The anisotropic Besov space is characterized by direction-dependent smoothness and involves several function classes as special cases. The results indicate that it is possible to alleviate the curse of dimensionality when the true function has high anisotropic smoothness. To evaluate the performance of the proposed method, numerical experiments and real data analysis are conducted.
