  In this paper we introduce a family of stochastic gradient estimation
techniques based of the perturbative expansion around the mean of the sampling
distribution. We characterize the bias and variance of the resulting
Taylor-corrected estimators using the Lagrange error formula. Furthermore, we
introduce a family of variance reduction techniques that can be applied to
other gradient estimators. Finally, we show that these new perturbative methods
can be extended to discrete functions using analytic continuation. Using this
technique, we derive a new gradient descent method for training stochastic
networks with binary weights. In our experiments, we show that the perturbative
correction improves the convergence of stochastic variational inference both in
the continuous and in the discrete case.
