This is "propertional to" because we do not compute the normalising constant E[ log p(X, V) | V ]. This does not matter since this function is used to check that each EM M-step maximizes this quantity w.r.t \theta.
1 2 | complete_log_posterior(X, V, Vvar, W, mu, sigSq, K, sparse = FALSE,
b = NULL)
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