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Simplify LDA input parameterization #143

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Simplify LDA input parameterization #143

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30 changes: 17 additions & 13 deletions misc/cluster/lda/corr-lda.stan
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Expand Up @@ -2,28 +2,26 @@ 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
int<lower=0> corpus[M,V]; // word freq matrix, doc x word
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
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]);
theta[m] = softmax(eta[m]);
for (m in 1:K) {
Sigma[m,m] <- sigma[m] * sigma[m] * Omega[m,m];
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Thanks for replacing <- --- that would be a good change for the original model, as well as replacing increment_log_prob with target +=.

square(sigma[m]) will be a bit more efficient, as would be sigma[m]^2.

Sigma[m,m] = sigma[m] * sigma[m] * Omega[m,m];
for (n in (m+1):K) {
Sigma[m,n] <- sigma[m] * sigma[n] * Omega[m,n];
Sigma[n,m] <- Sigma[m,n];
Sigma[m,n] = sigma[m] * sigma[n] * Omega[m,n];
Sigma[n,m] = Sigma[m,n];
}
}
}
Expand All @@ -38,10 +36,16 @@ model {
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]]);
increment_log_prob(log_sum_exp(gamma)); // likelihood
for (i in 1:M) {
for (j in 1:V) {
int count = corpus[i,j];
real gamma[K];
if (count > 0) {
for (k in 1:K) {
gamma[k] = (log(theta[i,k]) + log(phi[k,j]))*count;
}
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Rather than looping to define gamma, a one-liner will do it:

gamma = count * (log(theta[i, ]) + log(phi[, j]);

The loop works for the count == 0 case (though a bit ineffciently) but presumably there aren't any zero-length documents in well-formed data sets, so I'd just write replace this whole loop with:

for (i in 1:M)
  for (j in 1:V)
    target += log_sum_exp(count * (log(theta[i, ]) + log(phi[, j]));

increment_log_prob is deprecated---this model has been around for a while without being updated.

increment_log_prob(log_sum_exp(gamma)); // likelihood
}
}
}
}
48 changes: 8 additions & 40 deletions misc/cluster/lda/lda.data.R
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Original file line number Diff line number Diff line change
Expand Up @@ -4,46 +4,14 @@ V <-
5
M <-
25
N <-
262
w <-
c(4L, 3L, 5L, 4L, 3L, 3L, 3L, 3L, 3L, 4L, 5L, 3L, 4L, 4L, 5L,
3L, 4L, 4L, 4L, 3L, 5L, 4L, 5L, 2L, 3L, 3L, 1L, 5L, 5L, 1L, 4L,
3L, 1L, 2L, 5L, 4L, 4L, 3L, 5L, 4L, 2L, 4L, 5L, 3L, 4L, 1L, 4L,
4L, 3L, 2L, 1L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 2L, 3L, 1L, 2L, 2L,
4L, 4L, 5L, 4L, 5L, 5L, 4L, 3L, 5L, 4L, 4L, 4L, 2L, 2L, 1L, 1L,
2L, 1L, 3L, 1L, 2L, 1L, 1L, 1L, 3L, 2L, 3L, 3L, 5L, 4L, 5L, 4L,
3L, 5L, 4L, 2L, 2L, 2L, 1L, 3L, 2L, 1L, 3L, 1L, 3L, 1L, 1L, 2L,
1L, 2L, 2L, 4L, 4L, 4L, 5L, 5L, 4L, 4L, 5L, 4L, 3L, 3L, 3L, 1L,
3L, 3L, 4L, 2L, 1L, 3L, 4L, 4L, 5L, 4L, 4L, 4L, 3L, 4L, 3L, 4L,
5L, 1L, 2L, 1L, 3L, 2L, 1L, 1L, 2L, 3L, 3L, 3L, 3L, 4L, 1L, 4L,
4L, 4L, 4L, 3L, 4L, 4L, 1L, 2L, 2L, 3L, 3L, 1L, 1L, 4L, 1L, 3L,
1L, 5L, 3L, 2L, 2L, 1L, 1L, 2L, 3L, 3L, 4L, 4L, 5L, 3L, 4L, 3L,
1L, 5L, 5L, 5L, 3L, 3L, 4L, 5L, 3L, 3L, 3L, 2L, 3L, 1L, 3L, 3L,
1L, 3L, 1L, 5L, 5L, 5L, 2L, 2L, 3L, 3L, 3L, 1L, 1L, 5L, 5L, 5L,
3L, 1L, 5L, 4L, 1L, 3L, 3L, 3L, 3L, 4L, 2L, 5L, 1L, 3L, 5L, 2L,
5L, 5L, 2L, 1L, 3L, 3L, 5L, 3L, 5L, 3L, 3L, 5L, 1L, 2L, 2L, 1L,
1L, 2L, 1L, 2L, 3L, 1L, 1L)
doc <-
c(1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L,
6L, 6L, 6L, 6L, 6L, 6L, 6L, 7L, 7L, 7L, 7L, 7L, 8L, 8L, 8L, 8L,
8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 9L, 9L, 9L, 9L,
9L, 9L, 9L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L,
10L, 10L, 10L, 10L, 10L, 10L, 11L, 11L, 11L, 11L, 11L, 11L, 12L,
12L, 12L, 12L, 13L, 13L, 13L, 13L, 13L, 13L, 13L, 13L, 13L, 14L,
14L, 14L, 14L, 14L, 14L, 14L, 14L, 14L, 14L, 14L, 15L, 15L, 15L,
15L, 15L, 15L, 15L, 15L, 15L, 15L, 15L, 16L, 16L, 16L, 16L, 16L,
16L, 16L, 16L, 16L, 16L, 17L, 17L, 17L, 17L, 17L, 17L, 17L, 17L,
17L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 19L, 19L,
19L, 19L, 19L, 19L, 19L, 19L, 19L, 20L, 20L, 20L, 20L, 20L, 20L,
20L, 20L, 20L, 21L, 21L, 21L, 21L, 21L, 21L, 21L, 21L, 21L, 21L,
22L, 22L, 22L, 22L, 22L, 22L, 22L, 22L, 23L, 23L, 23L, 23L, 23L,
23L, 23L, 23L, 23L, 23L, 24L, 24L, 24L, 24L, 24L, 24L, 24L, 24L,
24L, 24L, 24L, 24L, 24L, 24L, 24L, 24L, 24L, 24L, 24L, 24L, 24L,
25L, 25L, 25L, 25L, 25L, 25L, 25L, 25L, 25L, 25L, 25L)
corpus <-
structure(c(4, 1, 1, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 3, 3, 0,
1, 0, 0, 1, 4, 0, 1, 1, 1, 1, 6, 6, 0, 0, 1, 1, 0, 0, 1, 0, 0,
0, 3, 2, 1, 1, 1, 1, 0, 2, 1, 3, 2, 2, 5, 6, 1, 2, 6, 3, 1, 2,
3, 6, 1, 5, 1, 4, 6, 1, 3, 3, 3, 1, 2, 3, 2, 0, 1, 0, 0, 2, 4,
2, 7, 2, 1, 7, 0, 6, 2, 4, 0, 0, 1, 1, 1, 2, 2, 0, 0, 0, 1, 0,
2, 1, 0, 4, 7, 0, 1, 1, 3, 2, 4, 3, 3, 5, 0, 0, 1, 1, 2, 2, 0,
0, 0, 2), .Dim = c(25L, 5L))
alpha <-
c(0.5, 0.5)
beta <-
Expand Down
20 changes: 12 additions & 8 deletions misc/cluster/lda/lda.stan
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Original file line number Diff line number Diff line change
Expand Up @@ -2,9 +2,7 @@ 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
int<lower=0> corpus[M,V]; // word freq matrix, doc x word
vector<lower=0>[K] alpha; // topic prior
vector<lower=0>[V] beta; // word prior
}
Expand All @@ -17,10 +15,16 @@ model {
theta[m] ~ dirichlet(alpha); // prior
for (k in 1:K)
phi[k] ~ dirichlet(beta); // prior
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]]);
increment_log_prob(log_sum_exp(gamma)); // likelihood
for (i in 1:M) {
for (j in 1:V) {
int count = corpus[i,j];
real gamma[K];
if (count > 0) {
for (k in 1:K) {
gamma[k] <- (log(theta[i,k]) + log(phi[k,j]))*count;
}
increment_log_prob(log_sum_exp(gamma)); // likelihood
}
}
}
}
16 changes: 8 additions & 8 deletions misc/cluster/lda/sim-lda.R
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Expand Up @@ -8,6 +8,8 @@ phi <- array(NA,c(2,5));
phi[1,] = c(0.330, 0.330, 0.330, 0.005, 0.005);
phi[2,] = c(0.005, 0.005, 0.330, 0.330, 0.330);

set.seed(123)

M <- 25; # docs
avg_doc_length <- 10;
doc_length <- rpois(M,avg_doc_length);
Expand All @@ -18,16 +20,14 @@ beta <- rep(1/V,V);

theta <- rdirichlet(M,alpha);

w <- rep(NA,N);
doc <- rep(NA,N);
n <- 1;
corpus <- matrix(0, nrow = M, ncol = V);
for (m in 1:M) {
for (i in 1:doc_length[m]) {
z <- which(rmultinom(1,1,theta[m,]) == 1);
w[n] <- which(rmultinom(1,1,phi[z,]) == 1);
doc[n] <- m;
n <- n + 1;
topic_id <- which(rmultinom(1,1,theta[m,]) == 1);
word_id <- which(rmultinom(1,1,phi[topic_id,]) == 1);
corpus[m, word_id] = corpus[m, word_id] + 1;
}
}
stopifnot(all(rowSums(corpus) == doc_length));

dump(c("K","V","M","N","z","w","doc","alpha","beta"),"lda.data.R");
dump(c("K","V","M","corpus","alpha","beta"),"lda.data.R");