Variation Inference¶
Background: Bayesian Inference¶
Bayesian inference - Wikipedia
\[P(H|E) = \frac{P(E|H)\dot P(H)}{P(E)}\]
Variation Bayesian method¶
(NIPS 2016 Tutorial)Variational Inference: Foundations and Modern Methods
A probabilistic model is a joint distribution of hidden variables z and observed variables x,
\[p(z, x)\]
Inference about the unknowns is through the posterior, the conditional distribution of the hidden variables given the observations
\[p(z|x) = \frac{p(z,x)}{p(x)}\]
For most interesting models, the denominator is not tractable. We appeal to approximate posterior inference.