Variational Inference - Mean-Field Approximation

Mean-Field Approximation

The most common choice for $\mathcal{Q}$ is the mean-field family, which assumes the latents factorize:

$$q(z)=\prod _i{q}_i(z_i)$$

This makes coordinate-wise updates tractable: hold all $q_{j\ne i}$ fixed and optimize $q_i$ in closed form (this is coordinate ascent variational inference, CAVI). Mean-field is fast but biases the posterior toward independence — it cannot capture correlations between latents, which often makes it underestimate posterior variance.