Estimating the gradients of stochastic nodes is one of the crucial research
questions in the deep generative modeling community, which enables the gradient
descent optimization on neural network parameters. This estimation problem
becomes further complex when we regard the stochastic nodes to be discrete
because pathwise derivative techniques cannot be applied. Hence, the stochastic
gradient estimation of discrete distributions requires either a score function
method or continuous relaxation of the discrete random variables. This paper
proposes a general version of the Gumbel-Softmax estimator with continuous
relaxation, and this estimator is able to relax the discreteness of probability
distributions including more diverse types, other than categorical and
Bernoulli. In detail, we utilize the truncation of discrete random variables
and the Gumbel-Softmax trick with a linear transformation for the relaxed
reparameterization. The proposed approach enables the relaxed discrete random
variable to be reparameterized and to backpropagated through a large scale
stochastic computational graph. Our experiments consist of (1) synthetic data
analyses, which show the efficacy of our methods; and (2) applications on VAE
and topic model, which demonstrate the value of the proposed estimation in
practices