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#library(Rcpp); library(mvtnorm); library(msm); sourceCpp ("../src/cid.cpp"); source("CID-basefunctions.R");
# Single-membership Stochastic Block Model: Reference Class
#input: ID.labels for a number of nodes, chosen to be the "dominant" ones.
#output: the permutation to switch labels to a simpler convention.
draw.MMSB.from.nodes <- function (edge.list, node.block) {
block.id <- sapply(c(edge.list), function(jj)
sample(1:nrow(node.block), 1, prob=node.block[,jj]))
matrix(block.id, ncol=2)
}
MMSBMcid <-
setRefClass(
"MMSBMcid",
fields = list(
n.groups="numeric",
#b.vector="numeric", b.vector.m="numeric", b.vector.v="numeric",
block.matrix="matrix",
block.matrix.m="matrix",
block.matrix.v="matrix",
symmetric.b="logical",
strong.block="logical", ## 2014-12-08, ACT -- should the diagonal always be greater?
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. Must fix later, but OK for now.
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),
# b.vector=rep(0, n.groups*(n.groups+1)/2),
# b.vector.m=rep(0, n.groups*(n.groups+1)/2),
# b.vector.v=rep(10000, n.groups*(n.groups+1)/2),
block.matrix=matrix(0, nrow=n.groups, ncol=n.groups),
block.matrix.m=matrix(0, nrow=n.groups, ncol=n.groups),
block.matrix.v=matrix(10000, nrow=n.groups, ncol=n.groups),
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),
strong.block=FALSE,
shift=0,
symmetric.b=TRUE,
#single.membership=FALSE,
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$b.vector <<- b.vector
# .self$b.vector.m <<- b.vector.m
# .self$b.vector.v <<- b.vector.v
.self$block.matrix <<- block.matrix
.self$block.matrix.m <<- block.matrix.m
.self$block.matrix.v <<- block.matrix.v
if (symmetric.b) {
b.block <- .self$block.matrix
b.block[u.diag(.self$n.groups)] <- b.block[l.diag(.self$n.groups)]
.self$block.matrix <<- as.matrix(b.block)
}
.self$symmetric.b <<- symmetric.b
.self$membership.edge <<- membership.edge
.self$membership.node <<- membership.node
.self$membership.alpha0 <<- membership.alpha0
.self$residual.variance <<- residual.variance
.self$restrict.and.shift <<- restrict.and.shift
#.self$single.membership <<- FALSE
.self$strong.block <<- strong.block
.self$group.pairs <<- makeEdgeListSelfies(n.groups)
.self$shift <<- shift
if (generate) .self$generate() else .self$outcome <<- outcome
rotate()
},
# center.me = function () if (restrict.and.shift) {
# shift <<- mean(b.vector)
# b.vector <<- b.vector - 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 ("MMSBM: Resetting number of groups to one less than the number of nodes.")
n.groups <<- n.nodes - 1
#b.vector <<- rep(0, n.groups*(n.groups+1)/2)
block.matrix <<- matrix(0, nrow=n.groups,ncol=n.groups)
membership.node <<- sample(n.groups, n.nodes, replace=TRUE)
membership.edge <<- draw.MMSB.from.nodes(edge.list, membership.node)
membership.alpha0 <<- membership.alpha0[1:n.groups]
}
if (ncol(membership.node) != n.nodes) {
message ("Reinitializing MMSBM Membership Fractions")
membership.node <<- rdirichlet.block (matrix(membership.alpha0, nrow=n.groups, ncol=n.nodes))
}
if (nrow(membership.edge) != nrow(edge.list)) {
message ("Reinitializing MMSBM Edge Memberships")
membership.edge <<- draw.MMSB.from.nodes(edge.list, membership.node)
}
rotate()
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.matrix=block.matrix,
membership.edge=membership.edge,
membership.node=membership.node)
class(out) <- "MMSBMout"
#if (include.name) out <- c("SBM", out)
out
},
show = function () {
#message("b.vector:"); print(b.vector)
message("block.matrix:"); print(block.matrix)
message("membership.edge:"); print(t(membership.edge))
message("membership.node:"); print(membership.node)
#message("mult.factor:"); print(mult.factor)
},
plot = function (memb=membership.node, block=block.matrix, ...) {
block.membership.plot (memb, block, node.labels=node.names, ...)
},
plot.network = function (color=outcome, ...) {
image.netplot (edge.list, color, node.labels=node.names, ...)
},
value = function () {
#sbm.matrix <- symBlock(b.vector)
#mult.factor*
block.matrix[membership.edge[,1] +
dim(block.matrix)[1]*(membership.edge[,2]-1)]
},
value.ext = function (parameters=pieces(), edges=1:nrow(edge.list)) { #slightly slower.
sbm.matrix <- parameters[[1]]
#parameters[[3]]*
sbm.matrix[parameters[[2]][edges,1] +
dim(sbm.matrix)[1]*(parameters[[2]][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 () {
membership.node <<-
rdirichlet.block (matrix(membership.alpha0, nrow=n.groups, ncol=n.nodes))
membership.edge <<- draw.MMSB.from.nodes(edge.list, membership.node)
block.matrix <<- matrix(rnorm(n.groups*n.groups, 0, 1), nrow=n.groups)
if (strong.block) {
pivots <- sapply(1:n.groups, function(kk) max (c(block.matrix[kk, -kk], block.matrix[-kk, kk])))
diag(block.matrix) <<- pivots + rexp(n.groups)
}
## b.vector <<- rnorm(n.groups*(n.groups+1)/2, 0, 0.5)
# rotate()
},
rotate = function () {
rotation <- MMSBM.ID.rotation(membership.node, n.groups)
membership.edge <<- matrix(rotation[c(membership.edge)], ncol=2)
membership.node <<- membership.node[rotation,]
block.matrix <<- SBM.rotate.block(block.matrix, rotation)
##b.vector <<- SBM.rotate.bvector(b.vector, rotation)
},
draw = function (verbose=0, as.if.single=FALSE) {
if (length(outcome) != nrow(edge.list)) stop ("MMSBM: outcome and edge.list have different lengths.")
#Hold me!
b.matrix <- block.matrix ##symBlock(b.vector)
b.block <- membership.edge
b.node <- membership.node
#if (verbose>1) print(b.memb)
# draw edge and node memberships. We can do them simultaneously for each node.
for (ii in sample(1:n.nodes)) {
lefty <- edge.list.rows[[ii]][which(edge.list[edge.list.rows[[ii]],1] == ii)]
righty <- edge.list.rows[[ii]][which(edge.list[edge.list.rows[[ii]],2] == ii)]
log.pp.mat <- t(sapply(1:n.groups, function(gg) {
b.block[lefty, 1] <- gg
b.block[righty, 2] <- gg
piece <- b.matrix[b.block[c(lefty,righty),1] +
(b.block[c(lefty,righty),2]-1)*n.groups]
dnorm(outcome[c(lefty,righty)], piece, sqrt(residual.variance), log=TRUE)
# + log(b.node[gg,ii])
}))
if (!as.if.single) {
#print("nAIS")
picks <- apply(log.pp.mat + log(b.node[,ii]), 2, function(cc) {
cc <- cc - max(cc); sample(1:n.groups, 1, prob=exp(cc))
})
if (length(lefty)>0) b.block[lefty,1] <- picks[1:length(lefty)]
if (length(righty)>0) b.block[righty,2] <- picks[length(lefty) + 1:length(righty)]
#node membership
counts <- sapply(1:n.groups, function(gg)
sum(membership.edge[,1]==gg & edge.list[,1]==ii) +
sum(membership.edge[,2]==gg & edge.list[,2]==ii))
b.node[,ii] <- rdirichlet.one (counts + membership.alpha0)
} else {
#print("AIS")
#assuming even prior odds on each group, but all memberships for a node are the same.
cc <- apply(log.pp.mat, 1, sum); cc <- cc - max(cc)
pick <- sample(1:n.groups, 1, prob=exp(cc))
if (length(lefty)>0) b.block[lefty,1] <- pick
if (length(righty)>0) b.block[righty,2] <- pick
b.node[,ii] <- 1/n.groups
}
}
# if (verbose>1) print(b.memb)
membership.edge <<- b.block
membership.node <<- b.node
for (ss in 1:n.groups)
for (rr in 1:n.groups) if (!symmetric.b | (symmetric.b & ss <= rr)) {
if (symmetric.b) {
picks <- unique(c(which(membership.edge[,1] == ss & membership.edge[,2] == rr),
which(membership.edge[,1] == rr & membership.edge[,2] == ss)))
} else {
picks <- unique(c(which(membership.edge[,1] == ss & membership.edge[,2] == rr)))
}
# picks <- which((b.memb[edge.list[,1]] == ss & b.memb[edge.list[,2]] == rr) |
# (b.memb[edge.list[,2]] == ss & b.memb[edge.list[,1]] == rr))
# } else {
# picks <- which(b.memb[edge.list[,1]] == ss & b.memb[edge.list[,2]] == rr)
# }
if (length(picks) > 0) {
var.b <- 1/(length(picks)/residual.variance + 1/block.matrix.v[ss,rr])
mean.b <- var.b*(sum(outcome[picks])/residual.variance + block.matrix.m[ss,rr]/block.matrix.v[ss,rr])
} else {var.b <- 0.5^2; mean.b <- 0}
if (!strong.block) {
output <- rnorm(1, mean.b, sqrt(var.b))
} else {
if (ss == rr) {
pivot <- max (c(block.matrix[ss, -ss], block.matrix[-ss, ss]))
output <- rtnorm(1, mean.b, sqrt(var.b), lower=pivot)
} else {
pivot <- min (c(block.matrix[ss, ss], block.matrix[rr, rr]))
output <- rtnorm(1, mean.b, sqrt(var.b), upper=pivot)
}
}
block.matrix[ss,rr] <<- output
if (symmetric.b) block.matrix[rr,ss] <<- output
}
#b.vector <<- sapply(1:length(b.vector), function(bb) {
# if (length(picks) > 0) {
# var.b <- 1/(length(picks)/residual.variance + 1/b.vector.v[bb])
# mean.b <- var.b*(sum(outcome[picks])/residual.variance + b.vector.m[bb]/b.vector.v[bb])
# output <- rnorm(1, mean.b, sqrt(var.b))
# } else output <- rnorm(1, 0, 0.5)
# output
#})
# if (restrict.and.shift) {center.me()}
# rotate()
},
gibbs.full = function (report.interval=0, draws=100, burnin=0, thin=1,
make.random.start=FALSE,
as.if.single=FALSE) {
out <- list()
if (make.random.start) random.start()
for (kk in 1:(draws*thin+burnin)) {
draw(as.if.single=as.if.single);
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("MMSBM ",index)
} else if (round(index)==index) {
if (report.interval > 0) if (index %% report.interval == 0) message("MMSBM burnin ",index)
}
}
return(out)
},
gibbs.value = function (gibbs.out) sapply(gibbs.out, function(gg) {
value.ext (gg)
}),
gibbs.summary = function (gibbs.out) {
membs <- matrix(apply(sapply(gibbs.out, function(gg) gg$membership.node), 1, mean), ncol=n.nodes)
colnames(membs) <- node.names
this.block.matrix <- matrix(apply(sapply(gibbs.out, function(gg) c(gg$block.matrix)), 1, mean),
nrow=n.groups)
#bvec <- apply(sapply(gibbs.out, function(gg) gg$b.vector), 1, mean)
return(list(membership.node=membs,
#b.vector=bvec,
block=this.block.matrix))
},
print.gibbs.summary = function (gibbs.sum) {
message ("Block membership mixes:")
print (gibbs.sum$membership.node)
message ("Block value matrix:")
print (gibbs.sum$block)
return()
},
gibbs.mean = function(gibbs.out) {
get.sum <- gibbs.summary(gibbs.out)
return(MMSBM(n.groups=n.groups,
n.nodes=n.nodes,
edge.list=edge.list,
edge.list.rows=edge.list.rows,
residual.variance=residual.variance,
outcome=outcome,
block.matrix=get.sum$block,
block.matrix.m=block.matrix.m,
block.matrix.v=block.matrix.v,
membership.alpha0=membership.alpha0,
membership.node=get.sum$membership.node,
strong.block=strong.block,
shift=shift,
symmetric.b=symmetric.b,
restrict.and.shift=restrict.and.shift))
},
gibbs.plot = function (gibbs.out, ...) {
get.sum <- gibbs.summary(gibbs.out)
plot (get.sum$membership.node,
get.sum$block,
main = "MMSBM Summary from Gibbs Sampler", ...)
},
gibbs.node.colors = function (gibbs.out, colors=(1:n.groups) + 1) {
rep("#DDDDFF", n.nodes)
#get.sum <- gibbs.summary(gibbs.out)
#return(colors[get.sum$modal.membership])
}
)
)
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