Generalized Gumbel-Softmax Gradient Estimator for Various Discrete Random Variables

Estimating the gradients of stochastic nodes is one of the crucial research questions in the deep generative modeling community. This estimation problem becomes further complex when we regard the stochastic nodes to be discrete because pathwise derivative techniques can not be applied. Hence, the gradient estimation requires the score function methods or the 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 broader types than the current practice. In detail, we utilize the truncation of discrete random variables and the Gumbel-Softmax trick with a linear transformation for the relaxation. The proposed approach enables the relaxed discrete random variable to be reparameterized and to backpropagate through a large scale stochastic neural network. Our experiments consist of synthetic data analyses, which show the efficacy of our methods, and topic model analyses, which demonstrates the value of the proposed estimation in practices.