To infer a multilayer representation of high-dimensional count vectors, we
propose the Poisson gamma belief network (PGBN) that factorizes each of its
layers into the product of a connection weight matrix and the nonnegative real
hidden units of the next layer. The PGBN's hidden layers are jointly trained
with an upward-downward Gibbs sampler, each iteration of which upward samples
Dirichlet distributed connection weight vectors starting from the first layer
(bottom data layer), and then downward samples gamma distributed hidden units
starting from the top hidden layer. The gamma-negative binomial process
combined with a layer-wise training strategy allows the PGBN to infer the width
of each layer given a fixed budget on the width of the first layer. The PGBN
with a single hidden layer reduces to Poisson factor analysis. Example results
on text analysis illustrate interesting relationships between the width of the
first layer and the inferred network structure, and demonstrate that the PGBN,
whose hidden units are imposed with correlated gamma priors, can add more
layers to increase its performance gains over Poisson factor analysis, given
the same limit on the width of the first layer.

利用 Poisson gamma 信仰网络 (PGBN) 因子化每一层，通过上下 Gibbs 采样器进行联合训练，实现对高维计数向量的多层表示