Neural Information Processing Systems http://nips.cc/

Reparameterization of variational auto-encoders with continuous random variables is an effective method for reducing the variance of their gradient estimates. In the discrete case, one can perform reparametrization using the Gumbel-Max trick, but the resulting objective relies on an \arg \max operation and is non-differentiable. In contrast to previous works which resort to \emph{softmax}-based relaxations, we propose to optimize it directly by applying the \emph{direct loss minimization} approach. Our proposal extends naturally to structured discrete latent variable models when evaluating the \arg \max operation is tractable. We demonstrate empirically the effectiveness of the direct loss minimization technique in variational autoencoders with both unstructured and structured discrete latent variables.