Expectation of the Log-Likelihood in Variational Inference (ELBO)

• : The Evidence Lower Bound (ELBO), which is optimized in variational inference.
• : The expected value under the approximate posterior distribution .
• : The joint log-probability of observed data and latent variables .
• : The log of the approximate posterior.
• The goal of this equation is to approximate the true posterior by maximizing the ELBO with respect to . This balances model fit (how well explains ) with complexity (how different is from ).