Working on a better, simpler toy example for the paper.

analysis/smallsim_new.R

@@ -157,6 +157,8 @@ p6 <- ggplot(pdat,aes(x = iter,y = elbo,color = init)) +
   theme_cowplot(font_size = 10)
 print(p6)
 
+stop()
+
 # Fit the LDA model, this time while simultaneously estimating the
 # Dirichlet prior on the topic proportions.
 lda_eb0 <- run_lda(X,fit0,numiter = 400,estimate.alpha = TRUE)

analysis/smallsim_newer.R

@@ -0,0 +1,92 @@
+# Note: k should be 3 or greater.
+simulate_correlated_loadings <- function (n, k) {
+  L <- matrix(0,n,k)
+  L[,1] <- runif(n,0,2)
+  for (i in 1:n) {
+    js <- sample(2:k,2)
+    j1 <- js[1]
+    j2 <- js[2]
+    L[i,j1] <- 1
+    L[i,j2] <- 0.1
+  }
+  return(normalize.rows(L))
+}
+
+# CORRELATED TOPICS SCENARIO
+set.seed(1)
+n <- 100
+L <- simulate_correlated_loadings(n,k)
+X <- simulate_multinom_counts(L,F,s)
+X <- X[,colSums(X > 0) > 0]
+
+# Compare this Structure plot to the one above---there is more mixing of
+# topics 3 and 4.
+p9 <- simdata_structure_plot(L,topic_colors)
+print(p9)
+
+fit0 <- fit_poisson_nmf(X,k,numiter = 20,method = "em",control = control)
+fit1 <- fit_poisson_nmf(X,fit0=fit0,numiter=180,method="em",control=control)
+fit2 <- fit_poisson_nmf(X,fit0=fit0,numiter=180,method="scd",control=control)
+fit0 <- poisson2multinom(fit0)
+fit1 <- poisson2multinom(fit1)
+fit2 <- poisson2multinom(fit2)
+p <- loadings_scatterplot(fit1$L,fit2$L,topic_colors,"em","scd")
+print(p)
+
+stop()
+
+# As before, we run the EM and SCD updates to fit the multinomial topic
+# model, with a twist that we perform another round of SCD updates after
+# running the EM updates. This will be explained shortly.
+fit0 <- fit_poisson_nmf(X,k,numiter = 20,method = "em",control = control)
+fit1 <- fit_poisson_nmf(X,fit0=fit0,numiter=780,method="em",control=control)
+fit2 <- fit_poisson_nmf(X,fit0=fit0,numiter=980,method="scd",control=control)
+fit3 <- fit_poisson_nmf(X,fit0=fit1,numiter=200,method="scd",control=control)
+fit1 <- fit_poisson_nmf(X,fit0=fit1,numiter=200,method="em",control=control)
+fit0 <- poisson2multinom(fit0)
+fit1 <- poisson2multinom(fit1)
+fit2 <- poisson2multinom(fit2)
+fit3 <- poisson2multinom(fit3)
+
+# In this second example, after initially making good progress, the EM
+# estimates remain far from the solution achieved by SCD even after
+# hundreds of EM updates. This isn't a case where the EM updates have
+# settled on a different local solution---the SCD updates quickly
+# "rescue" the EM estimates.
+pdat <- rbind(data.frame(iter   = 1:1000,
+                         loglik = fit1$progress$loglik.multinom,
+                         res    = fit1$progress$res,
+                         method = "em"),
+              data.frame(iter   = 1:1000,
+                         loglik = fit2$progress$loglik.multinom,
+                         res    = fit2$progress$res,
+                         method = "scd"),
+              data.frame(iter   = 800:1000,
+                         loglik = fit3$progress[800:1000,"loglik.multinom"],
+                         res    = fit3$progress[800:1000,"res"],
+   	                 method = "em+scd"))
+pdat <- subset(pdat,iter >= 20)
+pdat <- transform(pdat,
+		  iter   = iter - 20,
+                  loglik = max(loglik) - loglik + 0.1)
+p10 <- ggplot(pdat,aes(x = iter,y = loglik,color = method)) +
+  geom_line(size = 0.75) +
+  scale_y_continuous(trans = "log10") +
+  scale_color_manual(values = c("dodgerblue","darkorange","magenta")) +
+  labs(x = "iteration",y = "loglik difference") +
+  theme_cowplot(font_size = 10)
+p11 <- ggplot(pdat,aes(x = iter,y = res,color = method)) +
+  geom_line(size = 0.75) +
+  scale_color_manual(values = c("dodgerblue","darkorange","magenta")) +
+  ylim(0,10) +
+  labs(x = "iteration",y = "max KKT residual") +
+  theme_cowplot(font_size = 10)
+print(plot_grid(p10,p11))
+
+stop()
+
+# This large difference in likelihood is not due to a trivial difference
+# in solution---for example, there are many large differences in the
+# topic proportion estimates.
+p12 <- loadings_scatterplot(fit1$L,fit2$L,topic_colors,"em","scd")
+print(p12)