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#library(Rcpp); library(mvtnorm); library(msm); sourceCpp ("../src/cid.cpp"); source("CID-basefunctions.R");
# Hierarchical Block Model: Reference Class
# This adapts and extends the "Hierarchical Random Graph" model from Clauset, Moore and Newman 2008 in Nature.
closest.ancestor.from.parents <- function (parents.vector) {
#parents.vector=c(0,1,1,2,2)
nodes <- length(parents.vector)
history <- function(kk) {
out <- kk
while (parents.vector[kk] > 0) {kk <- parents.vector[kk]; out <- c(kk,out)}
return(out)
}
history.all <- lapply(1:length(parents.vector), history)
length.set <- sapply(history.all, length)
out.table <- array(0, c(nodes,nodes))
for (ii in 1:nodes)
for (jj in ii:nodes) {
ll <- min(length.set[ii], length.set[jj])
pick <- history.all[[ii]][max(which(history.all[[ii]][1:ll] ==
history.all[[jj]][1:ll]))]
out.table[ii,jj] <- out.table[jj,ii] <- pick
}
return(out.table)
}
HBMcid <-
setRefClass(
"HBMcid",
fields = list(
n.groups="numeric",
block.value="numeric",
block.value.m="numeric",
block.value.v="numeric",
membership="numeric",
tree.parent="numeric",
common.anc="matrix",
#membership.edge="matrix", #looks like edge list: has the membership number of each participant.
#membership.node="matrix", #each column is the Dirichlet distribution for each membership.
#membership.alpha0="numeric", #prior strength for the Dirichlet -- alpha0*vector(1)
shift="numeric",
restrict.and.shift="logical",
group.pairs="matrix",
#single.membership="logical",
#inherited from main.
node.names="character",
n.nodes="numeric",
outcome="numeric",
edge.list="matrix",
residual.variance="numeric",
edge.list.rows="list" #,
),
methods=list(
initialize = function (
n.groups=2,
n.nodes=10,
edge.list=make.edge.list(n.nodes),
edge.list.rows=row.list.maker(edge.list),
residual.variance=1,
outcome=numeric(0),
block.value=rep(0, n.groups), #*(n.groups+1)/2),
block.value.m=rep(0, n.groups), #*(n.groups+1)/2),
block.value.v=rep(10000, n.groups), #*(n.groups+1)/2),
membership=sample(n.groups, n.nodes, replace=TRUE),
tree.parent=c(0, sapply(1:(n.groups-1), function(gg) sample(gg, 1))),
#membership.alpha0=0.1,
#membership.node=rdirichlet.block (matrix(membership.alpha0, nrow=n.groups, ncol=n.nodes)),
#membership.edge=draw.MMSB.from.nodes(edge.list, membership.node),
shift=0,
restrict.and.shift=FALSE,
generate=FALSE
) {
.self$n.nodes <<- n.nodes
.self$edge.list <<- edge.list
.self$edge.list.rows <<- edge.list.rows
.self$node.names <<- as.character(1:.self$n.nodes)
.self$n.groups <<- n.groups
.self$block.value <<- block.value
.self$block.value.m <<- block.value.m
.self$block.value.v <<- block.value.v
if (n.groups != length(block.value)) stop(paste("block.value",paste(block.value,collapse=","),"does not have length specified by n.groups,",n.groups))
.self$membership <<- membership
.self$tree.parent <<- tree.parent
if (n.groups != length(tree.parent)) stop(paste("tree.parent",paste(tree.parent,collapse=","),"does not have length specified by n.groups,",n.groups))
.self$common.anc <<- closest.ancestor.from.parents(tree.parent)
.self$residual.variance <<- residual.variance
.self$restrict.and.shift <<- restrict.and.shift
#.self$single.membership <<- FALSE
.self$group.pairs <<- makeEdgeListSelfies(n.groups)
.self$shift <<- shift
if (generate) .self$generate() else .self$outcome <<- outcome
},
center.me = function () if (restrict.and.shift) {
shift <<- mean(block.value)
block.value <<- block.value - shift
},
reinitialize = function (n.nodes=NULL,
edge.list=NULL, node.names=NULL) {
if (!is.null(n.nodes)) n.nodes <<- n.nodes
if (!is.null(edge.list)) {
edge.list <<- edge.list
edge.list.rows <<- row.list.maker(edge.list)
}
if (n.groups > n.nodes) {
warning ("HBM: Resetting number of groups to one less than the number of nodes.")
n.groups <<- n.nodes - 1
membership <<- sample(n.groups, n.nodes, replace=TRUE)
block.value <<- block.value[1:n.groups]
}
if (length(membership) != n.nodes) {
message ("Reinitializing HBM Membership Vector")
membership <<- sample(n.groups, n.nodes, replace=TRUE)
}
if (!is.null(node.names)) {
if (length(node.names) == .self$n.nodes) node.names <<- node.names
} else node.names <<- as.character(1:.self$n.nodes)
},
pieces = function (include.name=FALSE) {
out <- list (block.value=block.value,
membership=membership,
tree.parent=tree.parent)
class(out) <- "HBMout"
out
},
show = function () {
message("block.value:"); print(block.value)
message("membership:"); print(membership)
message("tree.parent:"); print(tree.parent)
},
plot = function (memb=membership, tree.par=tree.parent, blockval=block.value) {
circular.dendrogram (memb, tree.par, blockval, node.labels=node.names)
},
plot.network = function (color=outcome, ...) {
image.netplot (edge.list, color, node.labels=node.names, ...)
},
value = function () {
#sbm.matrix <- symBlock(block.value)
block.value[common.anc[membership[edge.list[,1]] + n.groups*(membership[edge.list[,2]]-1)]]
},
value.ext = function (parameters=pieces(), edges=1:nrow(edge.list)) { #slightly slower.
common.anc.temp <- closest.ancestor.from.parents(parameters[[3]])
parameters[[1]][common.anc.temp[parameters[[2]][edge.list[edges,1]] + n.groups*(parameters[[2]][edge.list[edges,2]]-1)]]
},
generate = function () {outcome <<- rnorm(nrow(edge.list), value(), sqrt(residual.variance))},
log.likelihood = function(parameters=pieces(), edges=1:nrow(edge.list)) {
meanpart <- value.ext (parameters, edges)
sum(dnorm(outcome[edges], meanpart, sqrt(residual.variance), log=TRUE))
},
random.start = function () {
tree.parent <<- c(0, sapply(1:(n.groups-1), function(gg) sample(gg, 1)))
membership <<- sample(n.groups, n.nodes, replace=TRUE)
block.value <<- rnorm(n.groups, 0, 0.5)
},
rotate = function () {
rotation <- SBM.ID.rotation(membership, n.groups)
membership <<- rotation[membership]
block.value <<- block.value[rotation]
inv.rotation <- sapply(1:length(rotation), function(rr) which(rotation==rr))
tp.temp <- tree.parent[inv.rotation]
tp.temp[tp.temp>0] <- rotation[tp.temp[tp.temp>0]]
tree.parent <<- tp.temp
},
draw = function (verbose=0) {
if (length(outcome) != nrow(edge.list)) stop ("HBM: outcome and edge.list have different lengths.")
#Hold me!
b.memb <- membership
common.anc.temp <- closest.ancestor.from.parents (tree.parent)
# draw node memberships in random order, so we don't favor escapes of lower-order nodes.
for (ii in sample(1:n.nodes)) if (sum(b.memb==b.memb[ii]) + sum(tree.parent==b.memb[ii]) > 2) { #all internal nodes must have two children; can't let it leave if it would leave 1 remaining.
log.pp.vec <- sapply(1:n.groups, function(gg) {
b.memb[ii] <- gg
piece <- block.value[common.anc.temp[b.memb[edge.list[edge.list.rows[[ii]],1]] +
n.groups*(b.memb[edge.list[edge.list.rows[[ii]],2]]-1)]]
sum(dnorm(outcome[edge.list.rows[[ii]]], piece, sqrt(residual.variance), log=TRUE))
})
log.pp.vec <- log.pp.vec - max(log.pp.vec)
b.memb[ii] <- sample (1:n.groups, 1, prob=exp(log.pp.vec))
} else if (sum(b.memb != b.memb[ii]) > 0) { #if it would cause a problem, and it's an option, find a leaf on another internal node and propose a swap.
other.node <- sample((1:n.nodes)[b.memb != b.memb[ii]], 1)
b.memb.temp <- b.memb; b.memb.temp[ii] <- b.memb[other.node]; b.memb.temp[other.node] <- b.memb[ii]
rowset <- intersect(edge.list.rows[[ii]], edge.list.rows[[other.node]])
piece0 <- block.value[common.anc.temp[b.memb[edge.list[rowset,1]] +
n.groups*(b.memb[edge.list[rowset,2]]-1)]]
log.pp.0 <- sum(dnorm(outcome[rowset], piece0, sqrt(residual.variance), log=TRUE))
piece1 <- block.value[common.anc.temp[b.memb.temp[edge.list[rowset,1]] +
n.groups*(b.memb.temp[edge.list[rowset,2]]-1)]]
log.pp.1 <- sum(dnorm(outcome[rowset], piece1, sqrt(residual.variance), log=TRUE))
if (log.pp.1 - log.pp.0 > -rexp(1)) b.memb <- b.memb.temp #Standard Metropolis step.
}
membership <<- b.memb
#update block value.
edge.group <- common.anc.temp[membership[edge.list[,1]] + n.groups*(membership[edge.list[,2]]-1)]
block.value <<- sapply(1:length(block.value), function(bb) {
#common ancestor values
picks <- which(edge.group == bb)
if (length(picks) > 0) {
var.b <- 1/(length(picks)/residual.variance + 1/block.value.v[bb])
mean.b <- var.b*(sum(outcome[picks])/residual.variance +
block.value.m[bb]/block.value.v[bb])
output <- rnorm(1, mean.b, sqrt(var.b))
} else output <- rnorm(1, 0, 0.5)
})
#update tree structure. How do we do this? Find another internal node that is not its own descendant.
b.tree <- tree.parent
common.anc.temp <- closest.ancestor.from.parents (tree.parent)
for (gg in sample(1:n.groups)) {
possibles <- which(common.anc.temp[gg,] != gg)
if (length(possibles) > 1 & sum(membership==b.tree[gg]) + sum(b.tree==b.tree[gg]) > 2 ) {
log.pp.vec <- sapply(1:length(possibles), function(pp) {
b.tree[gg] <- possibles[pp]
common.anc.temp <- closest.ancestor.from.parents (b.tree)
piece <- block.value[common.anc.temp[membership[edge.list[,1]] +
n.groups*(membership[edge.list[,2]]-1)]]
sum(dnorm(outcome, piece, sqrt(residual.variance), log=TRUE))
})
log.pp.vec <- log.pp.vec - max(log.pp.vec)
b.tree[gg] <- sample (possibles, 1, prob=exp(log.pp.vec))
common.anc.temp <- closest.ancestor.from.parents (b.tree)
}
}
tree.parent <<- b.tree
common.anc <<- closest.ancestor.from.parents(tree.parent)
if (restrict.and.shift) {center.me()}
rotate()
},
gibbs.full = function (report.interval=0, draws=100, burnin=0, thin=1,
make.random.start=FALSE) {
out <- list()
if (make.random.start) random.start()
for (kk in 1:(draws*thin+burnin)) {
draw();
index <- (kk-burnin)/thin
if (kk > burnin & round(index)==index) {
out[[index]] <- c(pieces(), list(log.likelihood=log.likelihood()))
if (report.interval > 0) if (index %% report.interval == 0) message("HBM ",index)
}
}
return(out)
},
gibbs.value = function (gibbs.out) sapply(gibbs.out, function(gg) {
value.ext (gg)
}),
gibbs.summary = function (gibbs.out) {
#message("Note: HBM is not built for summaries over the posterior, only maximal draws.")
return(gibbs.out[[length(gibbs.out)]])
},
print.gibbs.summary = function (gibbs.out) {
get.sum <- gibbs.summary(gibbs.out)
message ("Last state of the Markov Chain: Membership")
print(get.sum$membership)
message ("Internal tree parents:")
print(get.sum$tree.parent)
message ("Block values:")
print(get.sum$block.value)
},
gibbs.mean = function(gibbs.out){
get.sum <- gibbs.summary(gibbs.out)
return(HBM(n.groups=n.groups,n.nodes=n.nodes,
edge.list=edge.list,
edge.list.rows=edge.list.rows,
residual.variance=residual.variance,
outcome=outcome,
block.value=get.sum$block.value,
block.value.m=block.value.m,
block.value.v=block.value.v,
membership=get.sum$membership,
tree.parent=get.sum$tree.parent,
shift=shift,
restrict.and.shift=restrict.and.shift))
},
gibbs.plot = function (gibbs.out) {
#message("Note: HBM is not built for summaries over the posterior, only maximal draws.")
#print(gibbs.out[[length(gibbs.out)]])
get.sum <- gibbs.summary(gibbs.out)
plot (get.sum$membership,
get.sum$tree.parent,
get.sum$block.value)
},
gibbs.node.colors = function (gibbs.out, colors=(1:n.groups) + 1) {
get.sum <- gibbs.summary(gibbs.out)
return(colors[get.sum$membership])
}
)
)
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