Summary This paper proposes a control variate (CV) for the discrete distribution's REINFORCE gradient estimator (RGE). The CV is based on the Concrete distribution (CD), a continuous relaxation of the discrete distribution that admits only biased Monte Carlo (MC) estimates of the discrete distribution's gradient. Yet, using the CD as a CV results in an *unbiased* estimator for a discrete random variable's (rv) path gradient as well as lower variance than the RGE (as expected). REBAR is derived by exploiting the REINFORCE estimator for the CD and by observing that given a discrete draw, the CD's continuous parameter (z, here) can be marginalized out. REBAR has some nice connections to other estimators for discrete rv gradients, including MuProp.

It is now well understood that machine learning models, trained on data without due care, often exhibit unfair and discriminatory behavior against certain populations. Traditional algorithmic fairness research has mainly focused on supervised learning tasks, particularly classification. While fairness in unsupervised learning has received some attention, the literature has primarily addressed fair representation learning of continuous embeddings. In this paper, we conversely focus on unsupervised learning using probabilistic graphical models with discrete latent variables. We develop a fair stochastic variational inference technique for the discrete latent variables, which is accomplished by including a fairness penalty on the variational distribution that aims to respect the principles of intersectionality, a critical lens on fairness from the legal, social science, and humanities literature, and then optimizing the variational parameters under this penalty. We first show the utility of our method in improving equity and fairness for clustering using na\"ive Bayes and Gaussian mixture models on benchmark datasets. To demonstrate the generality of our approach and its potential for real-world impact, we then develop a special-purpose graphical model for criminal justice risk assessments, and use our fairness approach to prevent the inferences from encoding unfair societal biases.

Neural latent variable models enable the discovery of interesting structure in speech audio data. This paper presents a comparison of two different approaches which are broadly based on predicting future time-steps or auto-encoding the input signal. Our study compares the representations learned by vq-vae and vq-wav2vec in terms of sub-word unit discovery and phoneme recognition performance. Results show that future time-step prediction with vq-wav2vec achieves better performance. The best system achieves an error rate of 13.22 on the ZeroSpeech 2019 ABX phoneme discrimination challenge.

Gradient estimation in models with discrete latent variables is a challenging problem, because the simplest unbiased estimators tend to have high variance. To counteract this, modern estimators either introduce bias, rely on multiple function evaluations, or use learned, input-dependent baselines. Thus, there is a need for estimators that require minimal tuning, are computationally cheap, and have low mean squared error. In this paper, we show that the variance of the straight-through variant of the popular Gumbel-Softmax estimator can be reduced through Rao-Blackwellization without increasing the number of function evaluations. This provably reduces the mean squared error. We empirically demonstrate that this leads to variance reduction, faster convergence, and generally improved performance in two unsupervised latent variable models.

Learning in models with discrete latent variables is challenging due to high variance gradient estimators. Generally, approaches have relied on control variates to reduce the variance of the REINFORCE estimator. Recent work \citep{jang2016categorical, maddison2016concrete} has taken a different approach, introducing a continuous relaxation of discrete variables to produce low-variance, but biased, gradient estimates. In this work, we combine the two approaches through a novel control variate that produces low-variance, \emph{unbiased} gradient estimates. Then, we introduce a modification to the continuous relaxation and show that the tightness of the relaxation can be adapted online, removing it as a hyperparameter.

Deep neural networks with discrete latent variables offer the promise of better symbolic reasoning, and learning abstractions that are more useful to new tasks. There has been a surge in interest in discrete latent variable models, however, despite several recent improvements, the training of discrete latent variable models has remained challenging and their performance has mostly failed to match their continuous counterparts. Recent work on vector quantized autoencoders (VQ-VAE) has made substantial progress in this direction, with its perplexity almost matching that of a VAE on datasets such as CIFAR-10. In this work, we investigate an alternate training technique for VQ-VAE, inspired by its connection to the Expectation Maximization (EM) algorithm. Training the discrete bottleneck with EM helps us achieve better image generation results on CIFAR-10, and together with knowledge distillation, allows us to develop a non-autoregressive machine translation model whose accuracy almost matches a strong greedy autoregressive baseline Transformer, while being 3.3 times faster at inference.