  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.
