// Quartets first , then triples.
private Set<Set<Integer>> estimateClustersSAG() {
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.setDepth(depth); // 1?
adjacencies = fas.searchMapOnly();
System.out.println("...done.");
}
List<Integer> _variables = new ArrayList<Integer>();
for (int i = 0; i < variables.size(); i++) _variables.add(i);
Set<Set<Integer>> pureClusters = findPureClusters(_variables, adjacencies);
for (Set<Integer> cluster : pureClusters) _variables.removeAll(cluster);
Set<Set<Integer>> mixedClusters =
findMixedClusters(_variables, unionPure(pureClusters), adjacencies);
Set<Set<Integer>> allClusters = new HashSet<Set<Integer>>(pureClusters);
allClusters.addAll(mixedClusters);
return allClusters;
}
/**
* Returns the set of nodes reachable from the given set of initial nodes in the given graph
* according to the criteria in the given legal pairs object.
*
* <p>A variable V is reachable from initialNodes iff for some variable X in initialNodes thers is
* a path U [X, Y1, ..., V] such that legalPairs.isLegalFirstNode(X, Y1) and for each [H1, H2, H3]
* as subpaths of U, legalPairs.isLegalPairs(H1, H2, H3).
*
* <p>The algorithm used is a variant of Algorithm 1 from Geiger, Verma, & Pearl (1990).
*
* @param initialNodes The nodes that reachability paths start from.
* @param legalPairs Specifies initial edges (given initial nodes) and legal edge pairs.
* @param c a set of vertices (intuitively, the set of variables to be conditioned on.
* @param d a set of vertices (intuitively to be used in tests of legality, for example, the set
* of ancestors of c).
* @param graph the graph with respect to which reachability is determined.
*/
public static Set<Node> getReachableNodes(
List<Node> initialNodes, LegalPairs legalPairs, List<Node> c, List<Node> d, Graph graph) {
HashSet<Node> reachable = new HashSet<Node>();
MultiKeyMap visited = new MultiKeyMap();
List<ReachabilityEdge> nextEdges = new LinkedList<ReachabilityEdge>();
for (Node x : initialNodes) {
List<Node> adjX = graph.getAdjacentNodes(x);
for (Node y : adjX) {
if (legalPairs.isLegalFirstEdge(x, y)) {
reachable.add(y);
nextEdges.add(new ReachabilityEdge(x, y));
visited.put(x, y, Boolean.TRUE);
}
}
}
while (nextEdges.size() > 0) {
List<ReachabilityEdge> currEdges = nextEdges;
nextEdges = new LinkedList<ReachabilityEdge>();
for (ReachabilityEdge edge : currEdges) {
Node x = edge.getFrom();
Node y = edge.getTo();
List<Node> adjY = graph.getAdjacentNodes(y);
for (Node z : adjY) {
if ((visited.get(y, z)) == Boolean.TRUE) {
continue;
}
if (legalPairs.isLegalPair(x, y, z, c, d)) {
reachable.add(z);
nextEdges.add(new ReachabilityEdge(y, z));
visited.put(y, z, Boolean.TRUE);
}
}
}
}
return reachable;
}
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;
}