private Set<Integer> unionPure(Set<Set<Integer>> pureClusters) {
Set<Integer> unionPure = new HashSet<Integer>();
for (Set<Integer> cluster : pureClusters) {
unionPure.addAll(cluster);
}
return unionPure;
}
private Set<Integer> triple(int n1, int n2, int n3) {
Set<Integer> triple = new HashSet<Integer>();
triple.add(n1);
triple.add(n2);
triple.add(n3);
if (triple.size() < 3)
throw new IllegalArgumentException(
"Triple elements must be unique: <" + n1 + ", " + n2 + ", " + n3 + ">");
return triple;
}
private boolean quartetVanishes(Set<Integer> quartet) {
if (quartet.size() != 4)
throw new IllegalArgumentException("Expecting a quartet, size = " + quartet.size());
Iterator<Integer> iter = quartet.iterator();
int x = iter.next();
int y = iter.next();
int z = iter.next();
int w = iter.next();
return testVanishing(x, y, z, w);
}
private Set<Integer> quartet(int x, int y, int z, int w) {
Set<Integer> set = new HashSet<Integer>();
set.add(x);
set.add(y);
set.add(z);
set.add(w);
if (set.size() < 4)
throw new IllegalArgumentException(
"Quartet elements must be unique: <" + x + ", " + y + ", " + z + ", " + w + ">");
return set;
}
private Graph convertToGraph(Set<Set<Integer>> allClusters) {
Set<Set<Node>> _clustering = new HashSet<Set<Node>>();
for (Set<Integer> cluster : allClusters) {
Set<Node> nodes = new HashSet<Node>();
for (int i : cluster) {
nodes.add(variables.get(i));
}
_clustering.add(nodes);
}
return convertSearchGraphNodes(_clustering);
}
private boolean clique(Set<Integer> cluster, Map<Node, Set<Node>> adjacencies) {
List<Integer> _cluster = new ArrayList<Integer>(cluster);
for (int i = 0; i < cluster.size(); i++) {
for (int j = i + 1; j < cluster.size(); j++) {
Node nodei = variables.get(_cluster.get(i));
Node nodej = variables.get(_cluster.get(j));
if (!adjacencies.get(nodei).contains(nodej)) {
return false;
}
}
}
return true;
}
private boolean pure(Set<Integer> quartet, List<Integer> variables) {
if (quartetVanishes(quartet)) {
for (int o : variables) {
if (quartet.contains(o)) continue;
for (int p : quartet) {
Set<Integer> _quartet = new HashSet<Integer>(quartet);
_quartet.remove(p);
_quartet.add(o);
if (!quartetVanishes(_quartet)) {
return false;
}
}
}
return significant(new ArrayList<Integer>(quartet));
}
return false;
}
@Test
public void test1() {
GeneralizedSemPm pm = makeTypicalPm();
print(pm);
Node x1 = pm.getNode("X1");
Node x2 = pm.getNode("X2");
Node x3 = pm.getNode("X3");
Node x4 = pm.getNode("X4");
Node x5 = pm.getNode("X5");
SemGraph graph = pm.getGraph();
List<Node> variablesNodes = pm.getVariableNodes();
print(variablesNodes);
List<Node> errorNodes = pm.getErrorNodes();
print(errorNodes);
try {
pm.setNodeExpression(x1, "cos(B1) + E_X1");
print(pm);
String b1 = "B1";
String b2 = "B2";
String b3 = "B3";
Set<Node> nodes = pm.getReferencingNodes(b1);
assertTrue(nodes.contains(x1));
assertTrue(!nodes.contains(x2) && !nodes.contains(x2));
Set<String> referencedParameters = pm.getReferencedParameters(x3);
print("Parameters referenced by X3 are: " + referencedParameters);
assertTrue(referencedParameters.contains(b1) && referencedParameters.contains(b2));
assertTrue(!(referencedParameters.contains(b1) && referencedParameters.contains(b3)));
Node e_x3 = pm.getNode("E_X3");
//
for (Node node : pm.getNodes()) {
Set<Node> referencingNodes = pm.getReferencingNodes(node);
print("Nodes referencing " + node + " are: " + referencingNodes);
}
for (Node node : pm.getVariableNodes()) {
Set<Node> referencingNodes = pm.getReferencedNodes(node);
print("Nodes referenced by " + node + " are: " + referencingNodes);
}
Set<Node> referencingX3 = pm.getReferencingNodes(x3);
assertTrue(referencingX3.contains(x4));
assertTrue(!referencingX3.contains(x5));
Set<Node> referencedByX3 = pm.getReferencedNodes(x3);
assertTrue(
referencedByX3.contains(x1)
&& referencedByX3.contains(x2)
&& referencedByX3.contains(e_x3)
&& !referencedByX3.contains(x4));
pm.setNodeExpression(x5, "a * E^X2 + X4 + E_X5");
Node e_x5 = pm.getErrorNode(x5);
graph.setShowErrorTerms(true);
assertTrue(e_x5.equals(graph.getExogenous(x5)));
pm.setNodeExpression(e_x5, "Beta(3, 5)");
print(pm);
assertEquals("Split(-1.5,-.5,.5,1.5)", pm.getParameterExpressionString(b1));
pm.setParameterExpression(b1, "N(0, 2)");
assertEquals("N(0, 2)", pm.getParameterExpressionString(b1));
GeneralizedSemIm im = new GeneralizedSemIm(pm);
print(im);
DataSet dataSet = im.simulateDataAvoidInfinity(10, false);
print(dataSet);
} catch (ParseException e) {
e.printStackTrace();
}
}
@Test
public void test4() {
// For X3
Map<String, String[]> templates = new HashMap<>();
templates.put(
"NEW(b) + NEW(b) + NEW(c) + NEW(c) + NEW(c)", new String[] {"X1", "X2", "X3", "X4", "X5"});
templates.put("NEW(X1) + NEW(b) + NEW(c) + NEW(c) + NEW(c)", new String[] {});
templates.put("$", new String[] {});
templates.put("TSUM($)", new String[] {"X1", "X2", "X3", "X4", "X5"});
templates.put("TPROD($)", new String[] {"X1", "X2", "X3", "X4", "X5"});
templates.put("TPROD($) + X2", new String[] {"X1", "X2", "X3", "X4", "X5"});
templates.put("TPROD($) + TSUM($)", new String[] {"X1", "X2", "X3", "X4", "X5"});
templates.put("tan(TSUM(NEW(a)*$))", new String[] {"X1", "X2", "X3", "X4", "X5"});
templates.put("Normal(0, 1)", new String[] {"X1", "X2", "X3", "X4", "X5"});
templates.put("Normal(m, s)", new String[] {"X1", "X2", "X3", "X4", "X5"});
templates.put("Normal(NEW(m), s)", new String[] {"X1", "X2", "X3", "X4", "X5"});
templates.put("Normal(NEW(m), NEW(s)) + m1 + s6", new String[] {"X1", "X2", "X3", "X4", "X5"});
templates.put("TSUM($) + a", new String[] {"X1", "X2", "X3", "X4", "X5"});
templates.put("TSUM($) + TSUM($) + TSUM($) + 1", new String[] {"X1", "X2", "X3", "X4", "X5"});
for (String template : templates.keySet()) {
GeneralizedSemPm semPm = makeTypicalPm();
print(semPm.getGraph().toString());
Set<Node> shouldWork = new HashSet<>();
for (String name : templates.get(template)) {
shouldWork.add(semPm.getNode(name));
}
Set<Node> works = new HashSet<>();
for (int i = 0; i < semPm.getNodes().size(); i++) {
print("-----------");
print(semPm.getNodes().get(i).toString());
print("Trying template: " + template);
String _template = template;
Node node = semPm.getNodes().get(i);
try {
_template = TemplateExpander.getInstance().expandTemplate(_template, semPm, node);
} catch (Exception e) {
print("Couldn't expand template: " + template);
continue;
}
try {
semPm.setNodeExpression(node, _template);
print("Set formula " + _template + " for " + node);
if (semPm.getVariableNodes().contains(node)) {
works.add(node);
}
} catch (Exception e) {
print("Couldn't set formula " + _template + " for " + node);
}
}
for (String parameter : semPm.getParameters()) {
print("-----------");
print(parameter);
print("Trying template: " + template);
String _template = template;
try {
_template = TemplateExpander.getInstance().expandTemplate(_template, semPm, null);
} catch (Exception e) {
print("Couldn't expand template: " + template);
continue;
}
try {
semPm.setParameterExpression(parameter, _template);
print("Set formula " + _template + " for " + parameter);
} catch (Exception e) {
print("Couldn't set formula " + _template + " for " + parameter);
}
}
assertEquals(shouldWork, works);
}
}
private Set<Set<Integer>> finishESeeds(Set<Set<Integer>> ESeeds) {
log("Growing Effect Seeds.", true);
Set<Set<Integer>> grown = new HashSet<Set<Integer>>();
List<Integer> _variables = new ArrayList<Integer>();
for (int i = 0; i < variables.size(); i++) _variables.add(i);
// Lax grow phase with speedup.
if (algType == AlgType.lax) {
Set<Integer> t = new HashSet<Integer>();
int count = 0;
int total = ESeeds.size();
do {
if (!ESeeds.iterator().hasNext()) {
break;
}
Set<Integer> cluster = ESeeds.iterator().next();
Set<Integer> _cluster = new HashSet<Integer>(cluster);
if (extraShuffle) {
Collections.shuffle(_variables);
}
for (int o : _variables) {
if (_cluster.contains(o)) continue;
List<Integer> _cluster2 = new ArrayList<Integer>(_cluster);
int rejected = 0;
int accepted = 0;
ChoiceGenerator gen = new ChoiceGenerator(_cluster2.size(), 2);
int[] choice;
while ((choice = gen.next()) != null) {
int n1 = _cluster2.get(choice[0]);
int n2 = _cluster2.get(choice[1]);
t.clear();
t.add(n1);
t.add(n2);
t.add(o);
if (!ESeeds.contains(t)) {
rejected++;
} else {
accepted++;
}
}
if (rejected > accepted) {
continue;
}
_cluster.add(o);
// if (!(avgSumLnP(new ArrayList<Integer>(_cluster)) > -10)) {
// _cluster.remove(o);
// }
}
// This takes out all pure clusters that are subsets of _cluster.
ChoiceGenerator gen2 = new ChoiceGenerator(_cluster.size(), 3);
int[] choice2;
List<Integer> _cluster3 = new ArrayList<Integer>(_cluster);
while ((choice2 = gen2.next()) != null) {
int n1 = _cluster3.get(choice2[0]);
int n2 = _cluster3.get(choice2[1]);
int n3 = _cluster3.get(choice2[2]);
t.clear();
t.add(n1);
t.add(n2);
t.add(n3);
ESeeds.remove(t);
}
if (verbose) {
System.out.println(
"Grown "
+ (++count)
+ " of "
+ total
+ ": "
+ variablesForIndices(new ArrayList<Integer>(_cluster)));
}
grown.add(_cluster);
} while (!ESeeds.isEmpty());
}
// Lax grow phase without speedup.
if (algType == AlgType.laxWithSpeedup) {
int count = 0;
int total = ESeeds.size();
// Optimized lax version of grow phase.
for (Set<Integer> cluster : new HashSet<Set<Integer>>(ESeeds)) {
Set<Integer> _cluster = new HashSet<Integer>(cluster);
if (extraShuffle) {
Collections.shuffle(_variables);
}
for (int o : _variables) {
if (_cluster.contains(o)) continue;
List<Integer> _cluster2 = new ArrayList<Integer>(_cluster);
int rejected = 0;
int accepted = 0;
//
ChoiceGenerator gen = new ChoiceGenerator(_cluster2.size(), 2);
int[] choice;
while ((choice = gen.next()) != null) {
int n1 = _cluster2.get(choice[0]);
int n2 = _cluster2.get(choice[1]);
Set<Integer> triple = triple(n1, n2, o);
if (!ESeeds.contains(triple)) {
rejected++;
} else {
accepted++;
}
}
//
if (rejected > accepted) {
continue;
}
// System.out.println("Adding " + o + " to " + cluster);
_cluster.add(o);
}
for (Set<Integer> c : new HashSet<Set<Integer>>(ESeeds)) {
if (_cluster.containsAll(c)) {
ESeeds.remove(c);
}
}
if (verbose) {
System.out.println("Grown " + (++count) + " of " + total + ": " + _cluster);
}
grown.add(_cluster);
}
}
// Strict grow phase.
if (algType == AlgType.strict) {
Set<Integer> t = new HashSet<Integer>();
int count = 0;
int total = ESeeds.size();
do {
if (!ESeeds.iterator().hasNext()) {
break;
}
Set<Integer> cluster = ESeeds.iterator().next();
Set<Integer> _cluster = new HashSet<Integer>(cluster);
if (extraShuffle) {
Collections.shuffle(_variables);
}
VARIABLES:
for (int o : _variables) {
if (_cluster.contains(o)) continue;
List<Integer> _cluster2 = new ArrayList<Integer>(_cluster);
ChoiceGenerator gen = new ChoiceGenerator(_cluster2.size(), 2);
int[] choice;
while ((choice = gen.next()) != null) {
int n1 = _cluster2.get(choice[0]);
int n2 = _cluster2.get(choice[1]);
t.clear();
t.add(n1);
t.add(n2);
t.add(o);
if (!ESeeds.contains(t)) {
continue VARIABLES;
}
// if (avgSumLnP(new ArrayList<Integer>(t)) < -10) continue
// CLUSTER;
}
_cluster.add(o);
}
// This takes out all pure clusters that are subsets of _cluster.
ChoiceGenerator gen2 = new ChoiceGenerator(_cluster.size(), 3);
int[] choice2;
List<Integer> _cluster3 = new ArrayList<Integer>(_cluster);
while ((choice2 = gen2.next()) != null) {
int n1 = _cluster3.get(choice2[0]);
int n2 = _cluster3.get(choice2[1]);
int n3 = _cluster3.get(choice2[2]);
t.clear();
t.add(n1);
t.add(n2);
t.add(n3);
ESeeds.remove(t);
}
if (verbose) {
System.out.println("Grown " + (++count) + " of " + total + ": " + _cluster);
}
grown.add(_cluster);
} while (!ESeeds.isEmpty());
}
// Optimized pick phase.
log("Choosing among grown Effect Clusters.", true);
for (Set<Integer> l : grown) {
ArrayList<Integer> _l = new ArrayList<Integer>(l);
Collections.sort(_l);
if (verbose) {
log("Grown: " + variablesForIndices(_l), false);
}
}
Set<Set<Integer>> out = new HashSet<Set<Integer>>();
List<Set<Integer>> list = new ArrayList<Set<Integer>>(grown);
// final Map<Set<Integer>, Double> pValues = new HashMap<Set<Integer>, Double>();
//
// for (Set<Integer> o : grown) {
// pValues.put(o, getP(new ArrayList<Integer>(o)));
// }
Collections.sort(
list,
new Comparator<Set<Integer>>() {
@Override
public int compare(Set<Integer> o1, Set<Integer> o2) {
// if (o1.size() == o2.size()) {
// double chisq1 = pValues.get(o1);
// double chisq2 = pValues.get(o2);
// return Double.compare(chisq2, chisq1);
// }
return o2.size() - o1.size();
}
});
// for (Set<Integer> o : list) {
// if (pValues.get(o) < alpha) continue;
// System.out.println(variablesForIndices(new ArrayList<Integer>(o)) + " p = " +
// pValues.get(o));
// }
Set<Integer> all = new HashSet<Integer>();
CLUSTER:
for (Set<Integer> cluster : list) {
// if (pValues.get(cluster) < alpha) continue;
for (Integer i : cluster) {
if (all.contains(i)) continue CLUSTER;
}
out.add(cluster);
// if (getPMulticluster(out) < alpha) {
// out.remove(cluster);
// continue;
// }
all.addAll(cluster);
}
return out;
}
private Void findSeeds() {
Tetrad tetrad = null;
List<Node> empty = new ArrayList();
if (variables.size() < 4) {
Set<Set<Integer>> ESeeds = new HashSet<Set<Integer>>();
}
Map<Node, Set<Node>> adjacencies;
if (depth == -2) {
adjacencies = new HashMap<Node, Set<Node>>();
for (Node node : variables) {
HashSet<Node> _nodes = new HashSet<Node>(variables);
_nodes.remove(node);
adjacencies.put(node, _nodes);
}
} else {
// System.out.println("Running PC adjacency search...");
Graph graph = new EdgeListGraph(variables);
Fas fas = new Fas(graph, indTest);
fas.setVerbose(false);
fas.setDepth(depth); // 1?
adjacencies = fas.searchMapOnly();
// System.out.println("...done.");
}
List<Integer> allVariables = new ArrayList<Integer>();
for (int i = 0; i < variables.size(); i++) allVariables.add(i);
log("Finding seeds.", true);
ChoiceGenerator gen = new ChoiceGenerator(allVariables.size(), 3);
int[] choice;
CHOICE:
while ((choice = gen.next()) != null) {
int n1 = allVariables.get(choice[0]);
int n2 = allVariables.get(choice[1]);
int n3 = allVariables.get(choice[2]);
Node v1 = variables.get(choice[0]);
Node v2 = variables.get(choice[1]);
Node v3 = variables.get(choice[2]);
Set<Integer> triple = triple(n1, n2, n3);
if (!clique(triple, adjacencies)) {
continue;
}
boolean EPure = true;
boolean CPure1 = true;
boolean CPure2 = true;
boolean CPure3 = true;
for (int o : allVariables) {
if (triple.contains(o)) {
continue;
}
Node v4 = variables.get(o);
tetrad = new Tetrad(v1, v2, v3, v4);
if (deltaTest.getPValue(tetrad) > alpha) {
EPure = false;
if (indTest.isDependent(v1, v4, empty)) {
CPure1 = false;
}
if (indTest.isDependent(v2, v4, empty)) {
CPure2 = false;
}
}
tetrad = new Tetrad(v1, v3, v2, v4);
if (deltaTest.getPValue(tetrad) > alpha) {
EPure = false;
if (indTest.isDependent(v3, v4, empty)) {
CPure3 = false;
}
}
if (!(EPure || CPure1 || CPure2 || CPure3)) {
continue CHOICE;
}
}
HashSet<Integer> _cluster = new HashSet<Integer>(triple);
if (verbose) {
log("++" + variablesForIndices(new ArrayList<Integer>(triple)), false);
}
if (EPure) {
ESeeds.add(_cluster);
}
if (!EPure) {
if (CPure1) {
Set<Integer> _cluster1 = new HashSet<Integer>(n2, n3);
_cluster1.addAll(CSeeds.get(n1));
CSeeds.set(n1, _cluster1);
}
if (CPure2) {
Set<Integer> _cluster2 = new HashSet<Integer>(n1, n3);
_cluster2.addAll(CSeeds.get(n2));
CSeeds.set(n2, _cluster2);
}
if (CPure3) {
Set<Integer> _cluster3 = new HashSet<Integer>(n1, n2);
_cluster3.addAll(CSeeds.get(n3));
CSeeds.set(n3, _cluster3);
}
}
}
return null;
}
private Set<List<Set<Integer>>> combineClusters(
Set<Set<Integer>> ESeeds, List<Set<Integer>> CSeeds) {
Set<Set<Integer>> EClusters = finishESeeds(ESeeds);
Set<Integer> Cs = new HashSet();
for (int i = 0; i < variables.size(); i++) Cs.add(i);
Set<Integer> Es = new HashSet();
for (Set<Integer> ECluster : EClusters) Es.addAll(ECluster);
Cs.removeAll(Es);
List<List<Set<Integer>>> Clusters = new ArrayList();
for (Set<Integer> ECluster : EClusters) {
List<Set<Integer>> newCluster = new ArrayList<Set<Integer>>();
newCluster.add(1, ECluster);
Clusters.add(newCluster);
}
List<Set<Integer>> EClustersArray = new ArrayList<Set<Integer>>();
for (Set<Integer> ECluster : EClusters) EClustersArray.add(ECluster);
for (Integer c : Cs) {
int match = -1;
int overlap = 0;
boolean pass = false;
for (int i = 0; i < EClusters.size(); i++) {
Set<Integer> ECluster = EClustersArray.get(i);
Set<Integer> intersection = ECluster;
intersection.retainAll(CSeeds.get(c));
int _overlap = intersection.size();
if (_overlap > overlap) {
overlap = _overlap;
match = i;
if (overlap / ECluster.size() > CIparameter) {
pass = true;
}
}
}
if (pass) {
List<Set<Integer>> modCluster = new ArrayList<Set<Integer>>();
Set<Integer> newCs = Clusters.get(match).get(0);
newCs.add(c);
modCluster.add(newCs);
modCluster.add(EClustersArray.get(match));
Clusters.set(match, modCluster);
}
}
Set<List<Set<Integer>>> ClusterSet = new HashSet<List<Set<Integer>>>(Clusters);
return ClusterSet;
}
// Finds clusters of size 3.
private Set<Set<Integer>> findMixedClusters(
List<Integer> remaining, Set<Integer> unionPure, Map<Node, Set<Node>> adjacencies) {
Set<Set<Integer>> threeClusters = new HashSet<Set<Integer>>();
if (unionPure.isEmpty()) {
return new HashSet<Set<Integer>>();
}
REMAINING:
while (true) {
if (remaining.size() < 3) break;
ChoiceGenerator gen = new ChoiceGenerator(remaining.size(), 3);
int[] choice;
while ((choice = gen.next()) != null) {
int y = remaining.get(choice[0]);
int z = remaining.get(choice[1]);
int w = remaining.get(choice[2]);
Set<Integer> cluster = new HashSet<Integer>();
cluster.add(y);
cluster.add(z);
cluster.add(w);
// if (!allVariablesDependent(cluster)) {
// continue;
// }
if (!clique(cluster, adjacencies)) {
continue;
}
// Check all x as a cross check; really only one should be necessary.
boolean allX = true;
for (int x : unionPure) {
Set<Integer> _cluster = new HashSet<Integer>(cluster);
_cluster.add(x);
if (!quartetVanishes(_cluster) || !significant(new ArrayList<Integer>(_cluster))) {
allX = false;
break;
}
}
if (allX) {
threeClusters.add(cluster);
unionPure.addAll(cluster);
remaining.removeAll(cluster);
System.out.println(
"3-cluster found: " + variablesForIndices(new ArrayList<Integer>(cluster)));
continue REMAINING;
}
}
break;
}
return threeClusters;
}
// Trying to optimize the search for 4-cliques a bit.
private Set<Set<Integer>> findPureClusters2(
List<Integer> _variables, Map<Node, Set<Node>> adjacencies) {
System.out.println("Original variables = " + variables);
Set<Set<Integer>> clusters = new HashSet<Set<Integer>>();
List<Integer> allVariables = new ArrayList<Integer>();
Set<Node> foundVariables = new HashSet<Node>();
for (int i = 0; i < this.variables.size(); i++) allVariables.add(i);
for (int x : _variables) {
Node nodeX = variables.get(x);
if (foundVariables.contains(nodeX)) continue;
List<Node> adjX = new ArrayList<Node>(adjacencies.get(nodeX));
adjX.removeAll(foundVariables);
if (adjX.size() < 3) continue;
for (Node nodeY : adjX) {
if (foundVariables.contains(nodeY)) continue;
List<Node> commonXY = new ArrayList<Node>(adjacencies.get(nodeY));
commonXY.retainAll(adjX);
commonXY.removeAll(foundVariables);
for (Node nodeZ : commonXY) {
if (foundVariables.contains(nodeZ)) continue;
List<Node> commonXZ = new ArrayList<Node>(commonXY);
commonXZ.retainAll(adjacencies.get(nodeZ));
commonXZ.removeAll(foundVariables);
for (Node nodeW : commonXZ) {
if (foundVariables.contains(nodeW)) continue;
if (!adjacencies.get(nodeY).contains(nodeW)) {
continue;
}
int y = variables.indexOf(nodeY);
int w = variables.indexOf(nodeW);
int z = variables.indexOf(nodeZ);
Set<Integer> cluster = quartet(x, y, z, w);
// Note that purity needs to be assessed with respect to all of the variables in order
// to
// remove all latent-measure impurities between pairs of latents.
if (pure(cluster, allVariables)) {
O:
for (int o : _variables) {
if (cluster.contains(o)) continue;
cluster.add(o);
if (!clique(cluster, adjacencies)) {
cluster.remove(o);
continue O;
}
// if (!allVariablesDependent(cluster)) {
// cluster.remove(o);
// continue O;
// }
List<Integer> _cluster = new ArrayList<Integer>(cluster);
ChoiceGenerator gen2 = new ChoiceGenerator(_cluster.size(), 4);
int[] choice2;
int count = 0;
while ((choice2 = gen2.next()) != null) {
int x2 = _cluster.get(choice2[0]);
int y2 = _cluster.get(choice2[1]);
int z2 = _cluster.get(choice2[2]);
int w2 = _cluster.get(choice2[3]);
Set<Integer> quartet = quartet(x2, y2, z2, w2);
// Optimizes for large clusters.
if (quartet.contains(o)) {
if (++count > 2) continue O;
}
if (quartet.contains(o) && !pure(quartet, allVariables)) {
cluster.remove(o);
continue O;
}
}
}
System.out.println(
"Cluster found: " + variablesForIndices(new ArrayList<Integer>(cluster)));
clusters.add(cluster);
foundVariables.addAll(variablesForIndices(new ArrayList<Integer>(cluster)));
}
}
}
}
}
return clusters;
}
// Finds clusters of size 4 or higher.
private Set<Set<Integer>> findPureClusters(
List<Integer> _variables, Map<Node, Set<Node>> adjacencies) {
// System.out.println("Original variables = " + variables);
Set<Set<Integer>> clusters = new HashSet<Set<Integer>>();
List<Integer> allVariables = new ArrayList<Integer>();
for (int i = 0; i < this.variables.size(); i++) allVariables.add(i);
VARIABLES:
while (!_variables.isEmpty()) {
if (_variables.size() < 4) break;
for (int x : _variables) {
Node nodeX = variables.get(x);
List<Node> adjX = new ArrayList<Node>(adjacencies.get(nodeX));
adjX.retainAll(variablesForIndices(new ArrayList<Integer>(_variables)));
for (Node node : new ArrayList<Node>(adjX)) {
if (adjacencies.get(node).size() < 3) {
adjX.remove(node);
}
}
if (adjX.size() < 3) {
continue;
}
ChoiceGenerator gen = new ChoiceGenerator(adjX.size(), 3);
int[] choice;
while ((choice = gen.next()) != null) {
Node nodeY = adjX.get(choice[0]);
Node nodeZ = adjX.get(choice[1]);
Node nodeW = adjX.get(choice[2]);
int y = variables.indexOf(nodeY);
int w = variables.indexOf(nodeW);
int z = variables.indexOf(nodeZ);
Set<Integer> cluster = quartet(x, y, z, w);
if (!clique(cluster, adjacencies)) {
continue;
}
// Note that purity needs to be assessed with respect to all of the variables in order to
// remove all latent-measure impurities between pairs of latents.
if (pure(cluster, allVariables)) {
// Collections.shuffle(_variables);
O:
for (int o : _variables) {
if (cluster.contains(o)) continue;
cluster.add(o);
List<Integer> _cluster = new ArrayList<Integer>(cluster);
if (!clique(cluster, adjacencies)) {
cluster.remove(o);
continue O;
}
// if (!allVariablesDependent(cluster)) {
// cluster.remove(o);
// continue O;
// }
ChoiceGenerator gen2 = new ChoiceGenerator(_cluster.size(), 4);
int[] choice2;
int count = 0;
while ((choice2 = gen2.next()) != null) {
int x2 = _cluster.get(choice2[0]);
int y2 = _cluster.get(choice2[1]);
int z2 = _cluster.get(choice2[2]);
int w2 = _cluster.get(choice2[3]);
Set<Integer> quartet = quartet(x2, y2, z2, w2);
// Optimizes for large clusters.
if (quartet.contains(o)) {
if (++count > 50) continue O;
}
if (quartet.contains(o) && !pure(quartet, allVariables)) {
cluster.remove(o);
continue O;
}
}
}
System.out.println(
"Cluster found: " + variablesForIndices(new ArrayList<Integer>(cluster)));
clusters.add(cluster);
_variables.removeAll(cluster);
continue VARIABLES;
}
}
}
break;
}
return clusters;
}
