Definition

Stochastic variational inference uses stochastic estimates of the ELBO gradient, typically based on Monte Carlo samples or minibatches, instead of exact full gradients.

Gradient idea

$$\nabla_\phi \mathcal L(\phi) \approx \frac{1}{m}\sum_{i=1}^m \nabla_\phi \Big[ \log p(x,T(\epsilon_i,\phi)) - \log q_\phi(T(\epsilon_i,\phi)) \Big].$$