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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 ).