Nonlinear Sufficient Dimension Reduction with a Stochastic Neural Network
Authors: SIQI LIANG, Yan Sun, Faming Liang

Sufficient dimension reduction is a powerful tool to extract core information hidden in the high-dimensional data and has potentially many important applications in machine learning tasks. However, the existing nonlinear sufficient dimension reduction  methods often lack the scalability necessary for dealing with large-scale data.  We propose a new type of stochastic neural network under a rigorous probabilistic framework and show that it can be used for sufficient dimension reduction for large-scale data. The proposed stochastic neural network is trained using an adaptive stochastic gradient Markov chain Monte Carlo algorithm, whose convergence is rigorously studied in the paper as well. Through extensive experiments on real-world classification and regression problems, we show that the proposed method compares favorably with the existing  state-of-the-art sufficient dimension reduction methods and is computationally more efficient for large-scale data.