  Discrete and especially binary random variables occur in many machine
learning models, notably in variational autoencoders with binary latent states
and in stochastic binary networks. When learning such models, a key tool is an
estimator of the gradient of the expected loss with respect to the
probabilities of binary variables. The straight-through (ST) estimator gained
popularity due to its simplicity and efficiency, in particular in deep networks
where unbiased estimators are impractical. Several techniques were proposed to
improve over ST while keeping the same low computational complexity:
Gumbel-Softmax, ST-Gumbel-Softmax, BayesBiNN, FouST. We conduct a theoretical
analysis of bias and variance of these methods in order to understand tradeoffs
and verify the originally claimed properties. The presented theoretical results
allow for better understanding of these methods and in some cases reveal
serious issues.
