variational inference

Variational inference is just treating inference as an optimization problem:

$$\min \int \log l(\theta )q(\theta )+D(Q,P)$$

$l(\theta )$ … likelihood function - probability of observing your data given parameters $\theta$
$q(\theta )$ … variational distribution - your approximation to the true posterior $p(\theta |\text{data})$
You usually choose $D$ as the KL-divergence. I.e. you maximize the likelihood of data from a stochastic model with an arbitrary prior.

baysian inference