Within many machine learning algorithms, a fundamental problem concerns efficient calculation of an unbiased gradient wrt parameters $\boldsymbol{\gamma}$ for expectation-based objectives $\mathbb{E}_{q_{\boldsymbol{\gamma}} (\boldsymbol{y})} [f (\boldsymbol{y}) ]$. Most existing methods either ($i$) suffer from high variance, seeking help from (often) complicated variance-reduction techniques; or ($ii$) they only apply to reparameterizable continuous random variables and employ a reparameterization trick. To address these limitations, we propose a General and One-sample (GO) gradient that ($i$) applies to many distributions associated with non-reparameterizable continuous {\em or} discrete random variables, and ($ii$) has the same low-variance as the reparameterization trick. We find that the GO gradient often works well in practice based on only one Monte Carlo sample (although one can of course use more samples if desired). Alongside the GO gradient, we develop a means of propagating the chain rule through distributions, yielding statistical back-propagation, coupling neural networks to common random variables.
a Rep-like gradient for non-reparameterizable continuous/discrete distributions; further generalized to deep probabilistic models, yielding statistical back-propagation Presents a gradient estimator for expectation-based objectives that is unbiased, has low variance, and applies to either continuous and discrete random variables. An improved method for computing derivates of the expectation, and a new gradient estimator of low variance that allows training of generative models in which observations or latent variables are discrete. Designs a low variance gradient for distributions associated with continuous or discrete random variables.