mixedMem (version 1.1.0)

computeELBO: Compute a lower bound on the log-likelihood (ELBO)

Description

computeELBO computes the variational 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

computeELBO returns the lower bound on the log-likelihood, a real number.

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 parameters ($\alpha$ and $\theta$) that be derived from Jensen's inequality:

$E_Q{\log[p(X,Z, \Lambda)]} - E_Q{\log[Q(Z, \Lambda|\phi, \delta)]} \le\log P(obs |\alpha, \theta) $