R/maxmin-pc.R
In vspinu/bnlearn: Bayesian network structure learning, parameter learning and inference
maxmin.pc.optimized = function(x, whitelist, blacklist, test,
alpha, B, strict, debug = FALSE) {
nodes = names(x)
mb = list()
for (node in nodes) {
backtracking = unlist(sapply(mb, function(x){ node %in% x$nbr }))
# 1. [Forward Phase (I)]
mb[[node]] = maxmin.pc.forward.phase(node, data = x, nodes = nodes,
alpha = alpha, B = B, whitelist = whitelist, blacklist = blacklist,
backtracking = backtracking, test = test, optimized = TRUE,
debug = debug)
# 2. [Backward Phase (II)]
mb[[node]] = neighbour(node, mb = mb, data = x, alpha = alpha,
B = B, whitelist = whitelist, blacklist = blacklist,
backtracking = backtracking, test = test, markov = FALSE, debug = debug)
}#FOR
# check neighbourhood sets for consistency.
mb = bn.recovery(mb, nodes = nodes, strict = strict, debug = debug)
return(mb)
}#MAXMIN.PC.OPTIMIZED
maxmin.pc.cluster = function(x, cluster, whitelist, blacklist,
test, alpha, B, strict, debug = FALSE) {
nodes = names(x)
# 1. [Forward Phase (I)]
mb = parLapply(cluster, as.list(nodes), maxmin.pc.forward.phase, data = x,
nodes = nodes, alpha = alpha, B = B, whitelist = whitelist,
blacklist = blacklist, test = test, optimized = FALSE, debug = debug)
names(mb) = nodes
# 2. [Backward Phase (II)]
mb = parLapply(cluster, as.list(nodes), neighbour, mb = mb, data = x,
alpha = alpha, B = B, whitelist = whitelist, blacklist = blacklist,
test = test, markov = FALSE, debug = debug)
names(mb) = nodes
# check neighbourhood sets for consistency.
mb = bn.recovery(mb, nodes = nodes, strict = strict, debug = debug)
return(mb)
}#MAXMIN.PC.CLUSTER
maxmin.pc = function(x, whitelist, blacklist, test, alpha, B,
strict, debug = FALSE) {
nodes = names(x)
# 1. [Forward Phase (I)]
mb = lapply(as.list(nodes), maxmin.pc.forward.phase, data = x, nodes = nodes,
alpha = alpha, B = B, whitelist = whitelist, blacklist = blacklist,
test = test, optimized = FALSE, debug = debug)
names(mb) = nodes
# 2. [Backward Phase (II)]
mb = lapply(as.list(nodes), neighbour, mb = mb, data = x, alpha = alpha,
B = B, whitelist = whitelist, blacklist = blacklist, test = test,
markov = FALSE, debug = debug)
names(mb) = nodes
# check neighbourhood sets for consistency.
mb = bn.recovery(mb, nodes = nodes, strict = strict, debug = debug)
return(mb)
}#MAXMIN.PC
maxmin.pc.forward.phase = function(x, data, nodes, alpha, B, whitelist,
blacklist, backtracking = NULL, test, optimized = TRUE, debug = FALSE) {
nodes = nodes[nodes != x]
known.good = known.bad = c()
whitelisted = nodes[sapply(nodes,
function(y) { is.whitelisted(whitelist, c(x, y), either = TRUE) })]
blacklisted = nodes[sapply(nodes,
function(y) { is.blacklisted(blacklist, c(x, y), both = TRUE) })]
cpc = c()
association = structure(numeric(length(nodes)), names = nodes)
to.add = ""
# growing phase
if (debug) {
cat("----------------------------------------------------------------\n")
cat("* forward phase for node", x, ".\n")
}#THEN
# whitelisted nodes are included, and blacklisted nodes are excluded.
cpc = whitelisted
nodes = nodes[!(nodes %in% c(cpc, blacklisted))]
# use backtracking for a further screening of the nodes to be checked.
if (!is.null(backtracking) && optimized) {
# nodes whose neighbourhood includes this node are included, because
# X \in NBR(Y) <=> Y \in NBR(X); they can be removed in the backward
# phase later on if they are false positives.
known.good = names(backtracking[backtracking])
cpc = unique(c(cpc, known.good))
# and vice versa X not adiacent to Y <=> Y not adiacent to X
known.bad = names(backtracking[!backtracking])
# from empirical observations, MMPC has very few false negatives and
# therefore it is fairly safe not to test known.bad nodes.
nodes = nodes[!(nodes %in% known.bad)]
if (debug) {
cat(" * known good (backtracking): '", known.good, "'.\n")
cat(" * known bad (backtracking): '", known.bad, "'.\n")
cat(" * nodes still to be tested for inclusion: '",
nodes[!(nodes %in% cpc)], "'.\n")
}#THEN
}#THEN
# phase I (stepwise forward selection)
repeat {
# do not check nodes which have a p-value above the alpha threshold, as
# it can only increase; also do not check 'known bad' ones.
to.be.checked = setdiff(names(which(association < alpha)), c(cpc, known.bad))
# get an association measure for each of the available nodes.
association = sapply(to.be.checked, maxmin.pc.heuristic.optimized, y = x,
sx = cpc, data = data, test = test, alpha = alpha, B = B,
association = association, debug = debug)
# stop if there are no candidates for inclusion.
if (all(association > alpha) || length(nodes) == 0 || is.null(nodes)) break
# get the one which maximizes the association measure.
to.add = names(which.min(association))
if (debug) {
cat(" @", to.add, "accepted as a parent/children candidate ( p-value:",
association[to.add], ").\n")
cat(" > current candidates are '", c(cpc, to.add), "'.\n")
}#THEN
if (association[to.add] <= alpha) {
cpc = c(cpc, to.add)
nodes = nodes[nodes != to.add]
}#THEN
}#REPEAT
return(cpc)
}#MAXMIN.PC.FORWARD.PHASE
maxmin.pc.heuristic.optimized = function(x, y, sx, data, test, alpha, B,
association, debug = FALSE) {
k = 0
min.assoc = association[x]
if (debug) {
cat(" * checking node", x ,"for association.\n")
cat(" > starting with association", min.assoc, ".\n")
}#THEN
# generate only the subsets of the current parent/children set
# which include node added last; the rest are considered to be
# already tested against.
last = sx[length(sx)]
sx = sx[-length(sx)]
repeat {
# create all the possible subsets of size k of the candidate
# parent-children set.
dsep.subsets = subsets(length(sx), k, sx)
for (s in 1:nrow(dsep.subsets)) {
a = conditional.test(x, y, c(dsep.subsets[s,], last), data = data,
test = test, B = B, alpha = alpha)
if (debug) {
cat(" > trying conditioning subset '", c(dsep.subsets[s,], last), "'.\n")
cat(" > node", x, "has p-value:", a, ".\n")
}#THEN
# minimum association means maximum p-value.
min.assoc = max(min.assoc, a)
# if the p-value is already this high, it's useless to do further
# testing (as it min.assoc can only increase in value).
if (min.assoc > alpha) break
}#FOR
# if the p-value is already this high, it's useless to do further
# testing (as it min.assoc can only increase in value).
if (min.assoc > alpha) break
if (k < length(sx))
k = k + 1
else
break
}#REPEAT
if (debug)
cat(" > node", x, "has a minimum association of",
min.assoc, ".\n")
return(min.assoc)
}#MAXMIN.PC.HEURISTIC.OPTIMIZED
vspinu/bnlearn documentation built on May 3, 2019, 7:08 p.m.
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maxmin.pc.optimized = function(x, whitelist, blacklist, test,
alpha, B, strict, debug = FALSE) {
nodes = names(x)
mb = list()
for (node in nodes) {
backtracking = unlist(sapply(mb, function(x){ node %in% x$nbr }))
# 1. [Forward Phase (I)]
mb[[node]] = maxmin.pc.forward.phase(node, data = x, nodes = nodes,
alpha = alpha, B = B, whitelist = whitelist, blacklist = blacklist,
backtracking = backtracking, test = test, optimized = TRUE,
debug = debug)
# 2. [Backward Phase (II)]
mb[[node]] = neighbour(node, mb = mb, data = x, alpha = alpha,
B = B, whitelist = whitelist, blacklist = blacklist,
backtracking = backtracking, test = test, markov = FALSE, debug = debug)
}#FOR
# check neighbourhood sets for consistency.
mb = bn.recovery(mb, nodes = nodes, strict = strict, debug = debug)
return(mb)
}#MAXMIN.PC.OPTIMIZED
maxmin.pc.cluster = function(x, cluster, whitelist, blacklist,
test, alpha, B, strict, debug = FALSE) {
nodes = names(x)
# 1. [Forward Phase (I)]
mb = parLapply(cluster, as.list(nodes), maxmin.pc.forward.phase, data = x,
nodes = nodes, alpha = alpha, B = B, whitelist = whitelist,
blacklist = blacklist, test = test, optimized = FALSE, debug = debug)
names(mb) = nodes
# 2. [Backward Phase (II)]
mb = parLapply(cluster, as.list(nodes), neighbour, mb = mb, data = x,
alpha = alpha, B = B, whitelist = whitelist, blacklist = blacklist,
test = test, markov = FALSE, debug = debug)
names(mb) = nodes
# check neighbourhood sets for consistency.
mb = bn.recovery(mb, nodes = nodes, strict = strict, debug = debug)
return(mb)
}#MAXMIN.PC.CLUSTER
maxmin.pc = function(x, whitelist, blacklist, test, alpha, B,
strict, debug = FALSE) {
nodes = names(x)
# 1. [Forward Phase (I)]
mb = lapply(as.list(nodes), maxmin.pc.forward.phase, data = x, nodes = nodes,
alpha = alpha, B = B, whitelist = whitelist, blacklist = blacklist,
test = test, optimized = FALSE, debug = debug)
names(mb) = nodes
# 2. [Backward Phase (II)]
mb = lapply(as.list(nodes), neighbour, mb = mb, data = x, alpha = alpha,
B = B, whitelist = whitelist, blacklist = blacklist, test = test,
markov = FALSE, debug = debug)
names(mb) = nodes
# check neighbourhood sets for consistency.
mb = bn.recovery(mb, nodes = nodes, strict = strict, debug = debug)
return(mb)
}#MAXMIN.PC
maxmin.pc.forward.phase = function(x, data, nodes, alpha, B, whitelist,
blacklist, backtracking = NULL, test, optimized = TRUE, debug = FALSE) {
nodes = nodes[nodes != x]
known.good = known.bad = c()
whitelisted = nodes[sapply(nodes,
function(y) { is.whitelisted(whitelist, c(x, y), either = TRUE) })]
blacklisted = nodes[sapply(nodes,
function(y) { is.blacklisted(blacklist, c(x, y), both = TRUE) })]
cpc = c()
association = structure(numeric(length(nodes)), names = nodes)
to.add = ""
# growing phase
if (debug) {
cat("----------------------------------------------------------------\n")
cat("* forward phase for node", x, ".\n")
}#THEN
# whitelisted nodes are included, and blacklisted nodes are excluded.
cpc = whitelisted
nodes = nodes[!(nodes %in% c(cpc, blacklisted))]
# use backtracking for a further screening of the nodes to be checked.
if (!is.null(backtracking) && optimized) {
# nodes whose neighbourhood includes this node are included, because
# X \in NBR(Y) <=> Y \in NBR(X); they can be removed in the backward
# phase later on if they are false positives.
known.good = names(backtracking[backtracking])
cpc = unique(c(cpc, known.good))
# and vice versa X not adiacent to Y <=> Y not adiacent to X
known.bad = names(backtracking[!backtracking])
# from empirical observations, MMPC has very few false negatives and
# therefore it is fairly safe not to test known.bad nodes.
nodes = nodes[!(nodes %in% known.bad)]
if (debug) {
cat(" * known good (backtracking): '", known.good, "'.\n")
cat(" * known bad (backtracking): '", known.bad, "'.\n")
cat(" * nodes still to be tested for inclusion: '",
nodes[!(nodes %in% cpc)], "'.\n")
}#THEN
}#THEN
# phase I (stepwise forward selection)
repeat {
# do not check nodes which have a p-value above the alpha threshold, as
# it can only increase; also do not check 'known bad' ones.
to.be.checked = setdiff(names(which(association < alpha)), c(cpc, known.bad))
# get an association measure for each of the available nodes.
association = sapply(to.be.checked, maxmin.pc.heuristic.optimized, y = x,
sx = cpc, data = data, test = test, alpha = alpha, B = B,
association = association, debug = debug)
# stop if there are no candidates for inclusion.
if (all(association > alpha) || length(nodes) == 0 || is.null(nodes)) break
# get the one which maximizes the association measure.
to.add = names(which.min(association))
if (debug) {
cat(" @", to.add, "accepted as a parent/children candidate ( p-value:",
association[to.add], ").\n")
cat(" > current candidates are '", c(cpc, to.add), "'.\n")
}#THEN
if (association[to.add] <= alpha) {
cpc = c(cpc, to.add)
nodes = nodes[nodes != to.add]
}#THEN
}#REPEAT
return(cpc)
}#MAXMIN.PC.FORWARD.PHASE
maxmin.pc.heuristic.optimized = function(x, y, sx, data, test, alpha, B,
association, debug = FALSE) {
k = 0
min.assoc = association[x]
if (debug) {
cat(" * checking node", x ,"for association.\n")
cat(" > starting with association", min.assoc, ".\n")
}#THEN
# generate only the subsets of the current parent/children set
# which include node added last; the rest are considered to be
# already tested against.
last = sx[length(sx)]
sx = sx[-length(sx)]
repeat {
# create all the possible subsets of size k of the candidate
# parent-children set.
dsep.subsets = subsets(length(sx), k, sx)
for (s in 1:nrow(dsep.subsets)) {
a = conditional.test(x, y, c(dsep.subsets[s,], last), data = data,
test = test, B = B, alpha = alpha)
if (debug) {
cat(" > trying conditioning subset '", c(dsep.subsets[s,], last), "'.\n")
cat(" > node", x, "has p-value:", a, ".\n")
}#THEN
# minimum association means maximum p-value.
min.assoc = max(min.assoc, a)
# if the p-value is already this high, it's useless to do further
# testing (as it min.assoc can only increase in value).
if (min.assoc > alpha) break
}#FOR
# if the p-value is already this high, it's useless to do further
# testing (as it min.assoc can only increase in value).
if (min.assoc > alpha) break
if (k < length(sx))
k = k + 1
else
break
}#REPEAT
if (debug)
cat(" > node", x, "has a minimum association of",
min.assoc, ".\n")
return(min.assoc)
}#MAXMIN.PC.HEURISTIC.OPTIMIZED
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