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Coordinate Ascent Mean-field Variational Inference (Univariate Gaussian Example)

suzyahyah.github.io · 1,507 words · saved by 1 readers

Model Preliminaries Variational Inference is used to approximate posterior densities for Bayesian models as an alternative strategy to MCMC.

Model Preliminaries Variational Inference is used to approximate posterior densities for Bayesian models as an alternative strategy to MCMC. Given a (joint) model, $p(X, Z)$, with latent variables $Z = z_1, … z_m$, and observations $X = x_1, .. x_n$. we are often interested in computing the posterior $p(Z|X)$, the probability of our latent variables given the data. Often the exact posterior $p(Z|X)$ is intractable to calculate. Thus we aim to optimise a different distribution $q$, from a family of convenient distributions $Q$ over the latent variables, and minimize the KL divergence to…

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