A0476
Title: Nonlinear functional regression by functional deep neural network with kernel embedding
Authors: Zhongjie Shi - The University of Hong Kong (Hong Kong) [presenting]
Abstract: With the rapid development of deep learning in various fields of science and technology, such as speech recognition, image classification, and natural language processing, recently, it has also been widely applied in functional data analysis (FDA) with some empirical success. However, due to the infinite-dimensional input, we need a powerful dimension reduction method for functional learning tasks, especially for nonlinear functional regression. Based on the idea of smooth kernel integral transformation, a functional deep neural network is proposed with an efficient and fully-data-dependent dimension reduction method. The architecture of the functional net consists of a kernel embedding step, an integral transformation with a data-dependent smooth kernel; a projection step, a dimension reduction by projection with eigenfunction basis based on the embedding kernel; and finally, an expressive deep ReLU neural network for the prediction. The utilization of smooth kernel embedding enables the functional net to be discretization invariant, efficient, and robust to noisy observations, capable of utilizing information in both input functions and response data and have a low requirement on the number of discrete points for unimpaired generalization performance. Theoretical analysis is conducted, including approximation error and generalization error analysis and numerical simulations to verify these advantages of the functional net.
