computeELBO: Compute a lower bound on the log-likelihood (ELBO)
Description
Computes the value of a lower bound on the log-likelihood, also called the ELBO, for a mixed membership model.
Usage
computeELBO(model)
Arguments
model
a mixedMemModel object created by the mixedMemModel constructor
Value
value of the lower bound on the log-likelihood
Details
The lower bound (ELBO) is the objective function in the variational EM algorithim. It is a function of the latent variables ($\phi$ and $\delta$) and the hyperparameters ($\alpha$ and $\theta$) and
can be derived by Jensen's inequality.
$P(obs |\alpha, \theta) \ge E_Q{\log[p(X,Z, \Lambda)]} - E_Q{\log[Q(Z, \Lambda|\phi, \delta)]}$