EDITED AFTER REBUTTAL PERIOD: The rebuttal addresses concerns 3 and 4. I like the plots in Figure 1' and suggest to include them in the paper, together with table 2'. Regarding concerns 1 and 2, I disagree with the authors' rebuttal in that Gumble-softmax (and related) approaches are "orthogonal" to the paper. As noted in the rebuttal, any model with categorical variables can be rewritten in terms of if/else statements. That is exactly what I had in mind when I wrote my initial review, which is why I suggested to include an experiment involving a model with categorical latent variables. In this paper, a VI stochastic gradient estimator for non-differentiable models is proposed.

The Adversarially Learned Mixture Model (AMM) is a generative model for unsupervised or semi-supervised data clustering. The AMM is the first adversarially optimized method to model the conditional dependence between inferred continuous and categorical latent variables. Experiments on the MNIST and SVHN datasets show that the AMM allows for semantic separation of complex data when little or no labeled data is available. The AMM achieves a state-of-the-art unsupervised clustering error rate of 2.86% on the MNIST dataset. A semi-supervised extension of the AMM yields competitive results on the SVHN dataset.

We propose a novel approach to train a multi-modal policy from mixed demonstrations without their behavior labels. We develop a method to discover the latent factors of variation in the demonstrations. Specifically, our method is based on the variational autoencoder with a categorical latent variable. The encoder infers discrete latent factors corresponding to different behaviors from demonstrations. The decoder, as a policy, performs the behaviors accordingly. Once learned, the policy is able to reproduce a specific behavior by simply conditioning on a categorical vector. We evaluate our method on three different tasks, including a challenging task with high-dimensional visual inputs. Experimental results show that our approach is better than various baseline methods and competitive with a multi-modal policy trained by ground truth behavior labels.

Categorical variables are a natural choice for representing discrete structure in the world. However, stochastic neural networks rarely use categorical latent variables due to the inability to backpropagate through samples. In this work, we present an efficient gradient estimator that replaces the non-differentiable sample from a categorical distribution with a differentiable sample from a novel Gumbel-Softmax distribution. This distribution has the essential property that it can be smoothly annealed into a categorical distribution. We show that our Gumbel-Softmax estimator outperforms state-of-the-art gradient estimators on structured output prediction and unsupervised generative modeling tasks with categorical latent variables, and enables large speedups on semi-supervised classification.