Description Usage Arguments Value Examples
Estimating restricted latent class models (RLCM) by MCMC sampling given pre-specified upper bound for (M) latent state dimension. This function performs MCMC sampling with user-specified options. NB:
add flexibility to specify other parameters as fixed (or partially fixed such as the rows of Q).
1 | sampler(dat, model_options, mcmc_options)
|
dat |
binary data matrix (row for observations and column for dimensions) |
model_options |
Specifying assumed model options:
The following are not updated if provided with fixed values
|
mcmc_options |
Options for MCMC algorithm:
|
posterior samples for quantities of interest. It is a list comprised of the following elements:
t_samp
z_samp
N_samp
keepers
indices of MCMC samples kept for inference; will be used
to see which ones to use for inference after n_burnin
.
H_star_samp
t_max+3
by m_max
binary matrix
alpha_samp
The following are recorded if they are not fixed in a priori:
Q_samp
theta_samp
psi_samp
p_samp
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 | ## Not run:
rm(list=ls())
library(rewind)
library(matrixStats)
library(ars)
#optional packages:
library(mcclust.ext) # http://wrap.warwick.ac.uk/71934/1/mcclust.ext_1.0.tar.gz
# color palette for heatmaps:
YlGnBu5 <- c('#ffffd9','#c7e9b4','#41b6c4','#225ea8','#081d58',"#092d94")
hmcols <- colorRampPalette(YlGnBu5)(256)
# simulate data:
L0 <- 100
options_sim0 <- list(N = 200, # sample size.
M = 3, # true number of machines.
L = L0, # number of antibody landmarks.
K = 8, # number of true components.
theta = rep(0.9,L0), # true positive rates.
psi = rep(0.1,L0), # false positive rates.
alpha1 = 1, # half of the people have the first machine.
frac = 0.2, # fraction of positive dimensions (L-2M) in Q.
#pop_frac = rep(1/K0,K0) # population prevalences.
pop_frac = c(rep(2,4),rep(1,4)) # population prevalences.
)
image(simulate_data(options_sim0,SETSEED = TRUE)$datmat,col=hmcols)
simu <- simulate_data(options_sim0, SETSEED=TRUE)
simu_dat <- simu$datmat
rle(simu$Z)
#
# visualize truth:
#
# plot_truth(simu,options_sim0)
#
# specifying options:
#
# model options:
m_max0 <- 5
model_options0 <- list(
n = nrow(simu_dat),
t_max = 40,
m_max = m_max0,
b = 1, # Dirichlet hyperparameter; in the functions above,
# we used "b" - also can be called "gamma"!.
#Q = simu$Q,
a_theta = replicate(L0, c(9,1)),
a_psi = replicate(L0, c(1,9)),
#theta = options_sim0$theta,
#psi = options_sim0$psi,
alpha = 0.1,
frac = 0.2,
#p_both = rep(0.5,3),#,c(0.5,0.5^2,0.5^3,0.5^4,0.5^5)
#p0 = rep(0.5,m_max0), # <--- this seems to make a difference in convergence.
log_pk = "function(k) {log(0.1) + (k-1)*log(0.9)}"# Geometric(0.1).
#Prior for the number of components.
)
# pre-compute the log of coefficients in MFM:
model_options0$log_v<-mfm_coefficients(eval(parse(text=model_options0$log_pk)),
model_options0$b,
model_options0$n,
model_options0$t_max+1)
# mcmc options:
mcmc_options0 <- list(
n_total = 200,
n_keep = 50,
n_split = 5,
print_mod = 10,
constrained = TRUE, # <-- need to write a manual about when these options are okay.
block_update_H = TRUE,
block_update_Q = !TRUE,
ALL_IN_ONE_START =!TRUE, # <--- TRUE for putting all subjects in one cluster,
# FALSE by starting from a hierechical clustering
# (complete linkage) and cut
# to produce floor(t_max/4). Consider this as a warm start.
MORE_SPLIT = TRUE,
print_Q = TRUE,
init_frac = c(0.51,0.99)
)
# run posterior algorithm for simulated data:
out <- sampler(simu_dat,model_options0,mcmc_options0)
###############################################################
## Posterior summaries:
###############################################################
out0 <- out
out <- postprocess_H_Q(out0)
#Z_SAMP_FOR_PLOT <- out$z_samp # <---- use pseudo-indicators for co-clustering.
# tend to be more granular.
Z_SAMP_FOR_PLOT <- out$z_sci_samp # <--- use scientific-cluster indicators.
# posterior co-clustering probabilities (N by N):
comat <- z2comat(Z_SAMP_FOR_PLOT)
image(1:options_sim0$N,1:options_sim0$N, comat,
xlab="Subjects",ylab="Subjects",col=hmcols,main="co-clustering")
for (k in 1:options_sim0$K){
abline(h=cumsum(rle(simu$Z)$lengths)[k]+0.5,lty=2)
abline(v=cumsum(rle(simu$Z)$lengths)[k]+0.5,lty=2)
}
# Summarize partition C:
## Approach 0: The maximum a posterior: issue - the space is huge (Bell number).
## Not implemented.
## Approach 1: Minimizing the least squared error between the co-clustering indicators
## and the posterior co-clustering probabilities; (Dahl 2006)
## Approach 2: Wade - estimate the best partition using posterior expected loss
## by variation of information (VI) metric.
nsamp_C <- dim(Z_SAMP_FOR_PLOT)[2]
z_Em <- rep(NA,nsamp_C)
par(mfrow=c(2,3))
## Approach 1:
for (iter in 1:nsamp_C){
z_Em[iter] <- norm(z2comat(Z_SAMP_FOR_PLOT[,iter,drop=FALSE])-comat,"F")
}
ind_dahl <- which.min(z_Em)
# plot 1:
image(1:options_sim0$N,1:options_sim0$N,
z2comat(Z_SAMP_FOR_PLOT[,ind_dahl,drop=FALSE]),col=hmcols,
main="Dahl (2006) - least squares to hat{pi}_ij")
for (k in 1:options_sim0$K){
abline(h=cumsum(rle(simu$Z)$lengths)[k]+0.5,lty=2)
abline(v=cumsum(rle(simu$Z)$lengths)[k]+0.5,lty=2)
}
## Approach 2 - use "mcclust.ext" pacakge:
# process the posterior samples of cluster indicators:
psm <- comp.psm(t(Z_SAMP_FOR_PLOT))
# point estimate using all methods:
bmf.VI <- minVI(psm,t(Z_SAMP_FOR_PLOT),method="all",include.greedy=TRUE)
summary(bmf.VI)
# plot 2:
image(1:options_sim0$N,1:options_sim0$N,
z2comat(matrix(bmf.VI$cl["avg",],ncol=1)),col=hmcols,
main="Wade clustering")
for (k in 1:options_sim0$K){
abline(h=cumsum(rle(simu$Z)$lengths)[k]+0.5,lty=2)
abline(v=cumsum(rle(simu$Z)$lengths)[k]+0.5,lty=2)
}
#heatmap(z2comat(bmf.VI$cl["avg",]),col=hmcols)
# credible sets as defined in Wade and Ghahramani 2017.
bmf.cb <- credibleball(bmf.VI$cl[1,],t(Z_SAMP_FOR_PLOT))
# plot 3:
image(1:options_sim0$N,1:options_sim0$N,
z2comat(matrix(bmf.cb$c.horiz[1,],ncol=1)),col=hmcols,
main="Wade credible ball - horizontal")
for (k in 1:options_sim0$K){
abline(h=cumsum(rle(simu$Z)$lengths)[k]+0.5,lty=2)
abline(v=cumsum(rle(simu$Z)$lengths)[k]+0.5,lty=2)
}
#heatmap(z2comat(bmf.cb$c.horiz),col=hmcols)
# plot 4:
image(1:options_sim0$N,1:options_sim0$N,
z2comat(matrix(bmf.cb$c.uppervert[1,],ncol=1)),col=hmcols,
main="Wade credible ball - upper vertical")
for (k in 1:options_sim0$K){
abline(h=cumsum(rle(simu$Z)$lengths)[k]+0.5,lty=2)
abline(v=cumsum(rle(simu$Z)$lengths)[k]+0.5,lty=2)
}
#heatmap(z2comat(bmf.cb$c.uppervert),col=hmcols)
# plot 5:
image(1:options_sim0$N,1:options_sim0$N,
z2comat(matrix(bmf.cb$c.lowervert,ncol=1)),col=hmcols,
main="Wade credible ball - lower vertical")
for (k in 1:options_sim0$K){
abline(h=cumsum(rle(simu$Z)$lengths)[k]+0.5,lty=2)
abline(v=cumsum(rle(simu$Z)$lengths)[k]+0.5,lty=2)
}
#heatmap(z2comat(bmf.cb$c.lowervert),col=hmcols)
#
# summarize Q (first need to transpose it)
#
# Approach 1: compute the error |QQ' - E[QQ'|Y]|_Frobneious
# Approach 2: compute the marginal co-activation probability
# P(\sum_m Q_ml >= 1, \sum_m Q_ml' >= 1) -
# This is invariant to the relabeling of latent states, or cluster labels.
nsamp_Q <- dim(out$Q_merge_samp)[3]
EQQ <- matrix(0,nrow=dim(out$Q_merge_samp)[2],
ncol=dim(out$Q_merge_samp)[2]) # L by L.
EQQ_binary <- EQQ
# Approach 1:
for (iter in 1:nsamp_Q){
A <- t(out$Q_merge_samp[,,iter])
EQQ <- (A%*%t(A)+EQQ*(iter-1))/iter # invariant to the row reordering of Q.
EQQ_binary <- 0+(A%*%t(A)>0)+EQQ_binary
}
# Approach 2:
EQQ_percent <- EQQ_binary/nsamp_Q
image(EQQ_percent,col=hmcols,main="co-activation patterns across L dimensions")
# Approach 1:
Q_Em <- rep(NA,nsamp_Q)
for (iter in 1:nsamp_Q){
A <- t(out$Q_merge_samp[,,iter])
Q_Em[iter] <- norm(A%*%t(A) - EQQ,"F")
}
plot(Q_Em,type="o",main="||QQ'-E[QQ'|Y]||")
# choose the indices minimizing the errors:
ind_of_Q <- which(Q_Em==min(Q_Em))
#
# visualize truth:
#
pdf(file.path("inst/example_figure/","bmf_truth.pdf"),width=12,height=6)
plot_truth(simu,options_sim0)
dev.off()
#
# visualize the individual latent states depending on whether Q is known or not.
#
if (!is.null(model_options0$Q)){ # <--- Q known.
H_res <- matrix(0,nrow=nrow(simu$datmat),ncol=sum(rowSums(model_options0$Q)!=0))
H_pat_res <- matrix(0,nrow=nrow(simu$datmat),ncol=dim(out$H_star_merge_samp)[3])
for (l in 1:dim(out$H_star_merge_samp)[3]){
tmp_mylist <- out$mylist_samp[,l]
tmp0 <- out$H_star_samp[tmp_mylist[match(out$z_samp[,l],tmp_mylist)],,l]
#<------ could be simpler!!!
tmp1 <- tmp0[,colSums(tmp0)!=0,drop=FALSE]
tmp <- tmp1[,order_mat_byrow(model_options0$Q[rowSums(model_options0$Q)!=0,
,drop=FALSE])$ord,drop=FALSE]
H_pat_res[,l] <- bin2dec_vec(tmp,LOG=FALSE)
H_res <- (tmp + H_res*(l-1))/l
}
apply(H_pat_res,1,table)
image(f(H_res))
} else{ # <---- Q unknown.
#
# This is the best estimated Q:
#
Q_merged <- out$Q_merge_samp[,,ind_of_Q[1]] # just picked one.
NROW_Q_PLOT <- nrow(Q_merged) # sum(rowSums(Q_merged)!=0)
Q_PLOT <- f(order_mat_byrow(Q_merged)$res) # t(Q_merged)
#f(order_mat_byrow(Q_merged[rowSums(Q_merged)!=0,,drop=FALSE])$res)
image(1:ncol(simu$datmat),1:NROW_Q_PLOT,
Q_PLOT,
main="Best Q (merged & ordered)",col=hmcols,
xlab="Dimension (1:L)",
ylab="Latent State (1:M)",yaxt="n",cex.lab=1.2)
for (k in 1:NROW_Q_PLOT){
abline(h=NROW_Q_PLOT-k+0.5,
lty=2,col="grey",lwd=2)
}
#
# Summarize H* and H*(Z) for individual predictions:
#
# If we compare it to H, then the clustering matters too, not
# just H^*.
#
# Approach: just obtain the H samples from those iterations with the best Q
# obtained above.
#
H_res <- matrix(0,nrow=nrow(simu$datmat),ncol=sum(rowSums(Q_merged)!=0))
H_pat_res <- matrix(0,nrow=nrow(simu$datmat),ncol=length(ind_of_Q))
# columns for the best indices.
# here ind_of_Q are those that minimized the Q loss.
for (l in seq_along(ind_of_Q)){
tmp_mylist <- out$mylist_samp[,ind_of_Q[l]]
tmp0 <- out$col_merged_H_star_samp[out$z_samp[,ind_of_Q[l]],,ind_of_Q[l]]
tmp1 <- tmp0[,colSums(tmp0)!=0,drop=FALSE]
tmp <- tmp1[,order_mat_byrow(Q_merged[rowSums(Q_merged)!=0,,
drop=FALSE])$ord,drop=FALSE]
H_pat_res[,l] <- bin2dec_vec(tmp,LOG=FALSE)
H_res <- (tmp + H_res*(l-1))/l
}
apply(H_pat_res,1,table)
pdf(file.path("inst/example_figure/",
"H_estimated_marginal_prob_vs_truth.pdf"),width=12,height=6)
par(mfrow=c(1,2))
image(f(H_res),col=hmcols,main="estimated marginal prob") # <--- get marg prob.
image(f(simu$Eta[,order_mat_byrow(simu$Q)$ord]),col=hmcols,main="truth")
dev.off()
# issues: the order of the rows of Q at ind_of_Q might be different, so need to order them.
}
# posterior distribution over the number of pseudo-clusters T: <-- scientific clusters?
plot(out$t_samp,type="l",ylab="T: #pseudo-clusters")
## individual predictions:
pdf(file.path("inst/example_figure/","individual_pred_simulation.pdf"),height=15,width=12)
par(mar=c(2,8,8,0),mfrow=c(2,1),oma=c(5,5,5,5))
for (i in 1:nrow(simu_dat)){
plot_individual_pred(apply(H_pat_res,1,table)[[i]]/sum(apply(H_pat_res,1,table)[[i]]),
1:model_options0$m_max,paste0("Obs ", i),asp=0.5)
}
dev.off()
# check positive rate estimates:
pdf(file.path("inst/example_figure/","check_PR_post_vs_prior.pdf"),width=12,height=6)
par(mfrow=c(5,2))
for (l in 1:L0){
par(mar=c(1,1,1,2))
baker::beta_plot(model_options0$a_psi[1,l],model_options0$a_psi[2,l])
hist(out$psi_samp[l,],add=TRUE,freq=FALSE)
legend("topright",legend = l)
baker::beta_plot(model_options0$a_theta[1,l],model_options0$a_theta[2,l])
hist(out$theta_samp[l,],add=TRUE,freq=FALSE)
}
dev.off()
pdf(file.path("inst/example_figure/","posterior_sci_cluster_number.pdf"),
width=10,height=6)
scatterhist(1:ncol(out$z_sci_samp),apply(out$z_sci_samp,2,
function(v){length(unique(v))}),
"Index","tilde{T}: #scientific clusters")
dev.off()
# posterior distribution of active/effective dimensions (machines):
pdf(file.path("inst/example_figure/","posterior_effective_machines_number.pdf"),
width=10,height=6)
plot(table(apply(out$col_merged_H_star_samp,c(3),
function(x) sum(colSums(x)>0)))/mcmc_options0$n_keep,
xlab = "Effect Number of Machines",xlim=c(1,model_options0$m_max),
ylab ="Posterior Probability",
main="",lwd=4)
dev.off()
image(f(simu$Q),col=hmcols)
image(f(simu$xi),col=hmcols)
pred_xi <- 0+(out$H_star_samp[out$z_samp[,ind_dahl],,ind_dahl]%*%
apply(out$Q_samp[,,ind_dahl],c(1,2),mean))>0.5
image(f(pred_xi),col=hmcols)
image(f(pred_xi- simu$xi),col=hmcols)
## End(Not run) # END OF DONT RUN.
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