  Low-variance gradient estimation is crucial for learning directed graphical
models parameterized by neural networks, where the reparameterization trick is
widely used for those with continuous variables. While this technique gives
low-variance gradient estimates, it has not been directly applicable to
discrete variables, the sampling of which inherently requires discontinuous
operations. We argue that the discontinuity can be bypassed by marginalizing
out the variable of interest, which results in a new reparameterization trick
for discrete variables. This reparameterization greatly reduces the variance,
which is understood by regarding the method as an application of common random
numbers to the estimation. The resulting estimator is theoretically guaranteed
to have a variance not larger than that of the likelihood-ratio method with the
optimal input-dependent baseline. We give empirical results for variational
learning of sigmoid belief networks.
