A1122
Title: Belted and ensembled neural network for linear and nonlinear sufficient dimension reduction
Authors: Bing Li - The Pennsylvania State University (United States) [presenting]
Abstract: A unified, flexible, and easy-to-implement framework of sufficient dimension reduction that can accommodate both linear and nonlinear dimension reduction is introduced, and both the conditional distribution and the conditional mean are the targets of estimation. This unified framework is achieved by a specially structured neural network - the belted and ensembled neural network (BENN) - that consists of a narrow latent layer, which is called the belt, and a family of transformations of the response, which is called the ensemble. By strategically placing the belt at different layers of the neural network, linear or nonlinear sufficient dimension reduction may be achieved, and by choosing the appropriate transformation families, dimension reduction is achieved for the conditional distribution or the conditional mean. Moreover, thanks to the advantage of the neural network, the method is very fast to compute, overcoming a computation bottleneck of the traditional sufficient dimension reduction estimators, which involves the inversion of a matrix of dimension either p or $n$. The algorithm and convergence rate of the method are developed, which is compared with existing sufficient dimension reduction methods and is applied to two data examples.
