### Without smoothing
#' @export
LDA = function(W, n_topics = 3, max_iter = 100, max_iter_E_step = 10, convergence_threshold=1e-6){
k = n_topics
V = ncol(W)
M = nrow(W)
alpha <- rep(1, k)
beta <- rdirichlet(k, rep(1, V))
gamma <- matrix((alpha + V/k), M, k)
phi <- array(0, dim = c(V, k, M))
likelihood = rep(NA, max_iter)
for(i in 1:max_iter){
# E step
obj = E_step(gamma, phi, alpha, beta, W, max_iter_E_step, convergence_threshold)
likelihood[i] = obj$likelihood
phi = obj$phi
gamma = obj$gamma
# M step
beta = update_beta(phi, W, k)
alpha = update_alpha(alpha, gamma, M)
if(i > 5){
alpha = update_alpha_vec(alpha, gamma, M)
}
cat(sprintf("Iteration %d of EM completed. Likelihood: %1.3f \n", i, likelihood[i]))
if(check_convergence(likelihood, i, convergence_threshold)) break
}
return(list(likelihood = likelihood[1:i], phi = obj$phi, gamma = obj$gamma, alpha = alpha, beta=beta))
}
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