added correlated topic model example to compile and patched doc

Author: Bob Carpenter

misc/cluster/lda/corr-lda.stan

@@ -0,0 +1,46 @@
+data {
+  int<lower=2> K;               // num topics
+  int<lower=2> V;               // num words
+  int<lower=1> M;               // num docs
+  int<lower=1> N;               // total word instances
+  int<lower=1,upper=V> w[N];    // word n
+  int<lower=1,upper=M> doc[N];  // doc ID for word n
+  vector<lower=0>[V] beta;      // word prior
+}
+parameters {
+  vector[K] mu;              // topic mean
+  corr_matrix[K] Omega;      // correlation matrix
+  vector<lower=0>[K] sigma;  // scales
+  vector[K] eta[M];           // logit topic dist for doc m
+  simplex[V] phi[K];         // word dist for topic k
+}
+transformed parameters {
+  simplex[K] theta[M];       // simplex topic dist for doc m
+  cov_matrix[K] Sigma;       // covariance matrix
+  for (m in 1:M)
+    theta[m] <- softmax(eta[m]);
+  for (m in 1:M) {
+    Sigma[m,m] <- sigma[m] * sigma[m] * Omega[m,m];
+    for (n in (m+1):M)
+      Sigma[m,n] <- sigma[m] * sigma[n] * Omega[m,n];
+  } 
+}
+model {
+  // priors
+  for (k in 1:K)  
+    phi[k] ~ dirichlet(beta);
+  mu ~ normal(0,5);
+  Omega ~ lkj_corr(2.0);
+  sigma ~ cauchy(0,5);
+  // topic distribution for docs
+  for (m in 1:M)
+    eta[m] ~ multi_normal(mu,Sigma);
+  // token probabilities
+  for (n in 1:N) {
+    real gamma[K];
+    for (k in 1:K) 
+      gamma[k] <- log(theta[doc[n],k]) + log(phi[k,w[n]]);
+    lp__ <- lp__ + log_sum_exp(gamma);  // likelihood
+  }
+
+}