/////////////////////////////////////////////////////////////////////////////
// set the sepSet of x and y to the minimal such subset of the given sepSet
// and remove the edge <x, y> if background knowledge allows
/////////////////////////////////////////////////////////////////////////////
private void setMinSepSet(List<Node> sepSet, Node x, Node y) {
// It is assumed that BK has been considered before calling this method
// (for example, setting independent1 and independent2 in ruleR0_RFCI)
/*
// background knowledge requires this edge
if (knowledge.noEdgeRequired(x.getNode(), y.getNode()))
{
return;
}
*/
List<Node> empty = Collections.emptyList();
boolean indep;
try {
indep = independenceTest.isIndependent(x, y, empty);
} catch (Exception e) {
indep = false;
}
if (indep) {
getSepsets().set(x, y, empty);
return;
}
int sepSetSize = sepSet.size();
for (int i = 1; i <= sepSetSize; i++) {
ChoiceGenerator cg = new ChoiceGenerator(sepSetSize, i);
int[] combination;
while ((combination = cg.next()) != null) {
List<Node> condSet = GraphUtils.asList(combination, sepSet);
try {
indep = independenceTest.isIndependent(x, y, condSet);
} catch (Exception e) {
indep = false;
}
if (indep) {
getSepsets().set(x, y, condSet);
return;
}
}
}
}
/** Constructs a new FCI search for the given independence test and background knowledge. */
public Rfci(IndependenceTest independenceTest) {
if (independenceTest == null || knowledge == null) {
throw new NullPointerException();
}
this.independenceTest = independenceTest;
this.variables.addAll(independenceTest.getVariables());
}
private boolean localMarkovIndep(Node x, Node y, Graph pattern, IndependenceTest test) {
List<Node> future = pattern.getDescendants(Collections.singletonList(x));
List<Node> boundary = pattern.getAdjacentNodes(x);
boundary.removeAll(future);
List<Node> closure = new ArrayList<>(boundary);
closure.add(x);
closure.remove(y);
if (future.contains(y) || boundary.contains(y)) return false;
return test.isIndependent(x, y, boundary);
}
/**
* Constructs a new FCI search for the given independence test and background knowledge and a list
* of variables to search over.
*/
public Rfci(IndependenceTest independenceTest, List<Node> searchVars) {
if (independenceTest == null || knowledge == null) {
throw new NullPointerException();
}
this.independenceTest = independenceTest;
this.variables.addAll(independenceTest.getVariables());
Set<Node> remVars = new HashSet<Node>();
for (Node node1 : this.variables) {
boolean search = false;
for (Node node2 : searchVars) {
if (node1.getName().equals(node2.getName())) {
search = true;
}
}
if (!search) {
remVars.add(node1);
}
}
this.variables.removeAll(remVars);
}
////////////////////////////////////////////
// RFCI Algorithm 4.4 (Colombo et al, 2012)
// Orient colliders
////////////////////////////////////////////
private void ruleR0_RFCI(List<Node[]> rTuples) {
List<Node[]> lTuples = new ArrayList<Node[]>();
List<Node> nodes = graph.getNodes();
///////////////////////////////
// process tuples in rTuples
while (!rTuples.isEmpty()) {
Node[] thisTuple = rTuples.remove(0);
Node i = thisTuple[0];
Node j = thisTuple[1];
Node k = thisTuple[2];
final List<Node> nodes1 = getSepset(i, k);
if (nodes1 == null) continue;
List<Node> sepSet = new ArrayList<Node>(nodes1);
sepSet.remove(j);
boolean independent1 = false;
if (knowledge.noEdgeRequired(i.getName(), j.getName())) // if BK allows
{
try {
independent1 = independenceTest.isIndependent(i, j, sepSet);
} catch (Exception e) {
independent1 = true;
}
}
boolean independent2 = false;
if (knowledge.noEdgeRequired(j.getName(), k.getName())) // if BK allows
{
try {
independent2 = independenceTest.isIndependent(j, k, sepSet);
} catch (Exception e) {
independent2 = true;
}
}
if (!independent1 && !independent2) {
lTuples.add(thisTuple);
} else {
// set sepSets to minimal separating sets
if (independent1) {
setMinSepSet(sepSet, i, j);
graph.removeEdge(i, j);
}
if (independent2) {
setMinSepSet(sepSet, j, k);
graph.removeEdge(j, k);
}
// add new unshielded tuples to rTuples
for (Node thisNode : nodes) {
List<Node> adjacentNodes = graph.getAdjacentNodes(thisNode);
if (independent1) // <i, ., j>
{
if (adjacentNodes.contains(i) && adjacentNodes.contains(j)) {
Node[] newTuple = {i, thisNode, j};
rTuples.add(newTuple);
}
}
if (independent2) // <j, ., k>
{
if (adjacentNodes.contains(j) && adjacentNodes.contains(k)) {
Node[] newTuple = {j, thisNode, k};
rTuples.add(newTuple);
}
}
}
// remove tuples involving either (if independent1) <i, j>
// or (if independent2) <j, k> from rTuples
Iterator<Node[]> iter = rTuples.iterator();
while (iter.hasNext()) {
Node[] curTuple = iter.next();
if ((independent1 && (curTuple[1] == i) && ((curTuple[0] == j) || (curTuple[2] == j)))
|| (independent2 && (curTuple[1] == k) && ((curTuple[0] == j) || (curTuple[2] == j)))
|| (independent1 && (curTuple[1] == j) && ((curTuple[0] == i) || (curTuple[2] == i)))
|| (independent2
&& (curTuple[1] == j)
&& ((curTuple[0] == k) || (curTuple[2] == k)))) {
iter.remove();
}
}
// remove tuples involving either (if independent1) <i, j>
// or (if independent2) <j, k> from lTuples
iter = lTuples.iterator();
while (iter.hasNext()) {
Node[] curTuple = iter.next();
if ((independent1 && (curTuple[1] == i) && ((curTuple[0] == j) || (curTuple[2] == j)))
|| (independent2 && (curTuple[1] == k) && ((curTuple[0] == j) || (curTuple[2] == j)))
|| (independent1 && (curTuple[1] == j) && ((curTuple[0] == i) || (curTuple[2] == i)))
|| (independent2
&& (curTuple[1] == j)
&& ((curTuple[0] == k) || (curTuple[2] == k)))) {
iter.remove();
}
}
}
}
///////////////////////////////////////////////////////
// orient colliders (similar to original FCI ruleR0)
for (Node[] thisTuple : lTuples) {
Node i = thisTuple[0];
Node j = thisTuple[1];
Node k = thisTuple[2];
List<Node> sepset = getSepset(i, k);
if (sepset == null) {
continue;
}
if (!sepset.contains(j) && graph.isAdjacentTo(i, j) && graph.isAdjacentTo(j, k)) {
if (!isArrowpointAllowed(i, j)) {
continue;
}
if (!isArrowpointAllowed(k, j)) {
continue;
}
graph.setEndpoint(i, j, Endpoint.ARROW);
graph.setEndpoint(k, j, Endpoint.ARROW);
printWrongColliderMessage(i, j, k, "R0_RFCI");
}
}
}
/**
* Runs PC starting with a complete graph over all nodes of the given conditional independence
* test, using the given independence test and knowledge and returns the resultant graph. The
* returned graph will be a pattern if the independence information is consistent with the
* hypothesis that there are no latent common causes. It may, however, contain cycles or
* bidirected edges if this assumption is not born out, either due to the actual presence of
* latent common causes, or due to statistical errors in conditional independence judgments.
*/
public Graph search() {
return search(independenceTest.getVariables());
}
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;
}