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);
}
private boolean existsUnblockedSemiDirectedPath(Node from, Node to, List<Node> cond, Graph G) {
Queue<Node> Q = new LinkedList<Node>();
Set<Node> V = new HashSet<Node>();
Q.offer(from);
V.add(from);
while (!Q.isEmpty()) {
Node t = Q.remove();
if (t == to) return true;
for (Node u : G.getAdjacentNodes(t)) {
Edge edge = G.getEdge(t, u);
Node c = Edges.traverseSemiDirected(t, edge);
if (c == null) continue;
if (cond.contains(c)) continue;
if (c == to) return true;
if (!V.contains(c)) {
V.add(c);
Q.offer(c);
}
}
}
return false;
}
/**
* Transforms a maximally directed pattern (PDAG) represented in graph <code>g</code> into an
* arbitrary DAG by modifying <code>g</code> itself. Based on the algorithm described in
* Chickering (2002) "Optimal structure identification with greedy search" Journal of Machine
* Learning Research. R. Silva, June 2004
*/
public static void pdagToDag(Graph g) {
Graph p = new EdgeListGraph(g);
List<Edge> undirectedEdges = new ArrayList<Edge>();
for (Edge edge : g.getEdges()) {
if (edge.getEndpoint1() == Endpoint.TAIL
&& edge.getEndpoint2() == Endpoint.TAIL
&& !undirectedEdges.contains(edge)) {
undirectedEdges.add(edge);
}
}
g.removeEdges(undirectedEdges);
List<Node> pNodes = p.getNodes();
do {
Node x = null;
for (Node pNode : pNodes) {
x = pNode;
if (p.getChildren(x).size() > 0) {
continue;
}
Set<Node> neighbors = new HashSet<Node>();
for (Edge edge : p.getEdges()) {
if (edge.getNode1() == x || edge.getNode2() == x) {
if (edge.getEndpoint1() == Endpoint.TAIL && edge.getEndpoint2() == Endpoint.TAIL) {
if (edge.getNode1() == x) {
neighbors.add(edge.getNode2());
} else {
neighbors.add(edge.getNode1());
}
}
}
}
if (neighbors.size() > 0) {
Collection<Node> parents = p.getParents(x);
Set<Node> all = new HashSet<Node>(neighbors);
all.addAll(parents);
if (!GraphUtils.isClique(all, p)) {
continue;
}
}
for (Node neighbor : neighbors) {
Node node1 = g.getNode(neighbor.getName());
Node node2 = g.getNode(x.getName());
g.addDirectedEdge(node1, node2);
}
p.removeNode(x);
break;
}
pNodes.remove(x);
} while (pNodes.size() > 0);
}
/**
* Step C of PC; orients colliders using specified sepset. That is, orients x *-* y *-* z as x *->
* y <-* z just in case y is in Sepset({x, z}).
*/
public Map<Triple, Double> findCollidersUsingSepsets(
SepsetProducer sepsetProducer, Graph graph, boolean verbose, IKnowledge knowledge) {
TetradLogger.getInstance().log("details", "Starting Collider Orientation:");
Map<Triple, Double> colliders = new HashMap<>();
System.out.println("Looking for colliders");
List<Node> nodes = graph.getNodes();
for (Node b : nodes) {
List<Node> adjacentNodes = graph.getAdjacentNodes(b);
if (adjacentNodes.size() < 2) {
continue;
}
ChoiceGenerator cg = new ChoiceGenerator(adjacentNodes.size(), 2);
int[] combination;
while ((combination = cg.next()) != null) {
Node a = adjacentNodes.get(combination[0]);
Node c = adjacentNodes.get(combination[1]);
// Skip triples that are shielded.
if (graph.isAdjacentTo(a, c)) {
continue;
}
List<Node> sepset = sepsetProducer.getSepset(a, c);
if (sepset == null) continue;
// if (sepsetProducer.getPValue() < 0.5) continue;
if (!sepset.contains(b)) {
if (verbose) {
// boolean dsep = this.dsep.isIndependent(a, c);
// System.out.println("QQQ p = " + independenceTest.getPValue() +
// " " + dsep);
System.out.println(
"\nCollider orientation <" + a + ", " + b + ", " + c + "> sepset = " + sepset);
}
colliders.put(new Triple(a, b, c), sepsetProducer.getPValue());
TetradLogger.getInstance()
.log("colliderOrientations", SearchLogUtils.colliderOrientedMsg(a, b, c, sepset));
}
}
}
TetradLogger.getInstance().log("details", "Finishing Collider Orientation.");
System.out.println("Done finding colliders");
return colliders;
}
private void addColliders(
Graph graph, final SepsetProducer sepsetProducer, IKnowledge knowledge) {
final Map<Triple, Double> collidersPs =
findCollidersUsingSepsets(sepsetProducer, graph, verbose, knowledge);
List<Triple> colliders = new ArrayList<>(collidersPs.keySet());
Collections.shuffle(colliders);
Collections.sort(
colliders,
new Comparator<Triple>() {
public int compare(Triple o1, Triple o2) {
return -Double.compare(collidersPs.get(o1), collidersPs.get(o2));
}
});
if (trueDag != null) {
for (Triple collider : colliders) {
Node a = collider.getX();
Node b = collider.getY();
Node c = collider.getZ();
List<Node> sep = trueDag.getSepset(a, c);
System.out.println(
"JJJ "
+ collider
+ " collider = "
+ (sep != null && !sep.contains(b))
+ " p = "
+ collidersPs.get(collider));
}
}
for (Triple collider : colliders) {
Node a = collider.getX();
Node b = collider.getY();
Node c = collider.getZ();
if (!(isArrowpointAllowed(a, b, knowledge) && isArrowpointAllowed(c, b, knowledge))) {
continue;
}
if (!graph.getEdge(a, b).pointsTowards(a) && !graph.getEdge(b, c).pointsTowards(c)) {
graph.setEndpoint(a, b, Endpoint.ARROW);
graph.setEndpoint(c, b, Endpoint.ARROW);
}
}
}
private void ruleR1(Graph skeleton, Graph graph, List<Node> nodes) {
for (Node node : nodes) {
SortedMap<Double, String> scoreReports = new TreeMap<Double, String>();
List<Node> adj = skeleton.getAdjacentNodes(node);
DepthChoiceGenerator gen = new DepthChoiceGenerator(adj.size(), adj.size());
int[] choice;
double maxScore = Double.NEGATIVE_INFINITY;
List<Node> parents = null;
while ((choice = gen.next()) != null) {
List<Node> _parents = GraphUtils.asList(choice, adj);
double score = score(node, _parents);
scoreReports.put(-score, _parents.toString());
if (score > maxScore) {
maxScore = score;
parents = _parents;
}
}
for (double score : scoreReports.keySet()) {
TetradLogger.getInstance()
.log(
"score",
"For " + node + " parents = " + scoreReports.get(score) + " score = " + -score);
}
TetradLogger.getInstance().log("score", "");
if (parents == null) {
continue;
}
if (normal(node, parents)) continue;
for (Node _node : adj) {
if (parents.contains(_node)) {
Edge parentEdge = Edges.directedEdge(_node, node);
if (!graph.containsEdge(parentEdge)) {
graph.addEdge(parentEdge);
}
}
}
}
}
/**
* @param node The variable node in question.
* @return the error node for the given node.
*/
public Node getErrorNode(Node node) {
if (errorNodes.contains(node)) {
return node;
}
int index = variableNodes.indexOf(node);
if (index == -1) {
throw new NullPointerException(
node
+ " is not a node in this model. Perhaps "
+ "it's another node with the same name.");
}
return errorNodes.get(index);
}
public static boolean existsLocalSepsetWithoutDet(
Node x, Node y, Node z, IndependenceTest test, Graph graph, int depth) {
Set<Node> __nodes = new HashSet<Node>(graph.getAdjacentNodes(x));
__nodes.addAll(graph.getAdjacentNodes(z));
__nodes.remove(x);
__nodes.remove(z);
List<Node> _nodes = new LinkedList<Node>(__nodes);
TetradLogger.getInstance()
.log("adjacencies", "Adjacents for " + x + "--" + y + "--" + z + " = " + _nodes);
int _depth = depth;
if (_depth == -1) {
_depth = 1000;
}
_depth = Math.min(_depth, _nodes.size());
for (int d = 0; d <= _depth; d++) {
if (_nodes.size() >= d) {
ChoiceGenerator cg2 = new ChoiceGenerator(_nodes.size(), d);
int[] choice;
while ((choice = cg2.next()) != null) {
List<Node> condSet = asList(choice, _nodes);
if (condSet.contains(y)) {
continue;
}
if (test.determines(condSet, y)) {
continue;
}
// LogUtils.getInstance().finest("Trying " + condSet);
if (test.isIndependent(x, z, condSet)) {
return true;
}
}
}
}
return false;
}
/**
* Step C of PC; orients colliders using specified sepset. That is, orients x *-* y *-* z as x *->
* y <-* z just in case y is in Sepset({x, z}).
*/
public static void orientCollidersUsingSepsets(SepsetMap set, Knowledge knowledge, Graph graph) {
TetradLogger.getInstance().log("info", "Starting Collider Orientation:");
// verifySepsetIntegrity(set, graph);
List<Node> nodes = graph.getNodes();
for (Node a : nodes) {
List<Node> adjacentNodes = graph.getAdjacentNodes(a);
if (adjacentNodes.size() < 2) {
continue;
}
ChoiceGenerator cg = new ChoiceGenerator(adjacentNodes.size(), 2);
int[] combination;
while ((combination = cg.next()) != null) {
Node b = adjacentNodes.get(combination[0]);
Node c = adjacentNodes.get(combination[1]);
// Skip triples that are shielded.
if (graph.isAdjacentTo(b, c)) {
continue;
}
List<Node> sepset = set.get(b, c);
if (sepset != null
&& !sepset.contains(a)
&& isArrowpointAllowed(b, a, knowledge)
&& isArrowpointAllowed(c, a, knowledge)) {
graph.setEndpoint(b, a, Endpoint.ARROW);
graph.setEndpoint(c, a, Endpoint.ARROW);
TetradLogger.getInstance()
.log("colliderOriented", SearchLogUtils.colliderOrientedMsg(b, a, c, sepset));
}
}
}
TetradLogger.getInstance().log("info", "Finishing Collider Orientation.");
}
public static CpcTripleType getCpcTripleType(
Node x, Node y, Node z, IndependenceTest test, int depth, Graph graph) {
// System.out.println("getCpcTripleType 1");
boolean existsSepsetContainingY = false;
boolean existsSepsetNotContainingY = false;
Set<Node> __nodes = new HashSet<Node>(graph.getAdjacentNodes(x));
__nodes.remove(z);
// System.out.println("getCpcTripleType 2");
List<Node> _nodes = new LinkedList<Node>(__nodes);
TetradLogger.getInstance()
.log("adjacencies", "Adjacents for " + x + "--" + y + "--" + z + " = " + _nodes);
// System.out.println("getCpcTripleType 3");
int _depth = depth;
if (_depth == -1) {
_depth = 1000;
}
_depth = Math.min(_depth, _nodes.size());
// System.out.println("getCpcTripleType 4");
for (int d = 0; d <= _depth; d++) {
// System.out.println("getCpcTripleType 5");
ChoiceGenerator cg = new ChoiceGenerator(_nodes.size(), d);
int[] choice;
while ((choice = cg.next()) != null) {
// System.out.println("getCpcTripleType 6");
List<Node> condSet = GraphUtils.asList(choice, _nodes);
// System.out.println("getCpcTripleType 7");
if (test.isIndependent(x, z, condSet)) {
if (condSet.contains(y)) {
existsSepsetContainingY = true;
} else {
existsSepsetNotContainingY = true;
}
}
}
}
// System.out.println("getCpcTripleType 8");
__nodes = new HashSet<Node>(graph.getAdjacentNodes(z));
__nodes.remove(x);
_nodes = new LinkedList<Node>(__nodes);
TetradLogger.getInstance()
.log("adjacencies", "Adjacents for " + x + "--" + y + "--" + z + " = " + _nodes);
// System.out.println("getCpcTripleType 9");
_depth = depth;
if (_depth == -1) {
_depth = 1000;
}
_depth = Math.min(_depth, _nodes.size());
// System.out.println("getCpcTripleType 10");
for (int d = 0; d <= _depth; d++) {
// System.out.println("getCpcTripleType 11");
ChoiceGenerator cg = new ChoiceGenerator(_nodes.size(), d);
int[] choice;
while ((choice = cg.next()) != null) {
List<Node> condSet = GraphUtils.asList(choice, _nodes);
if (test.isIndependent(x, z, condSet)) {
if (condSet.contains(y)) {
existsSepsetContainingY = true;
} else {
existsSepsetNotContainingY = true;
}
}
}
}
// System.out.println("getCpcTripleType 12");
if (existsSepsetContainingY == existsSepsetNotContainingY) {
return CpcTripleType.AMBIGUOUS;
} else if (!existsSepsetNotContainingY) {
return CpcTripleType.NONCOLLIDER;
} else {
return CpcTripleType.COLLIDER;
}
}
////////////////////////////////////////////
// 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");
}
}
}
public void setNodeExpression(Node node, String expressionString) throws ParseException {
if (node == null) {
throw new NullPointerException("Node was null.");
}
if (expressionString == null) {
// return;
throw new NullPointerException("Expression string was null.");
}
// Parse the expression. This could throw an ParseException, but that exception needs to handed
// up the
// chain, because the interface will need it.
ExpressionParser parser = new ExpressionParser();
Expression expression = parser.parseExpression(expressionString);
List<String> parameterNames = parser.getParameters();
// Make a list of parent names.
List<Node> parents = this.graph.getParents(node);
List<String> parentNames = new LinkedList<>();
for (Node parent : parents) {
parentNames.add(parent.getName());
}
// List<String> _params = new ArrayList<String>(parameterNames);
// _params.retainAll(variableNames);
// _params.removeAll(parentNames);
//
// if (!_params.isEmpty()) {
// throw new IllegalArgumentException("Conditioning on a variable other than the
// parents: " + node);
// }
// Make a list of parameter names, by removing from the parser's list of freeParameters any that
// correspond
// to parent variables. If there are any variable names (including error terms) that are not
// among the list of
// parents, that's a time to throw an exception. We must respect the graph! (We will not
// complain if any parents
// are missing.)
parameterNames.removeAll(variableNames);
for (Node variable : nodes) {
if (parameterNames.contains(variable.getName())) {
parameterNames.remove(variable.getName());
// throw new IllegalArgumentException("The list of parameter names may not
// include variables: " + variable.getName());
}
}
// Remove old parameter references.
List<String> parametersToRemove = new LinkedList<>();
for (String parameter : this.referencedParameters.keySet()) {
Set<Node> nodes = this.referencedParameters.get(parameter);
if (nodes.contains(node)) {
nodes.remove(node);
}
if (nodes.isEmpty()) {
parametersToRemove.add(parameter);
}
}
for (String parameter : parametersToRemove) {
this.referencedParameters.remove(parameter);
this.parameterExpressions.remove(parameter);
this.parameterExpressionStrings.remove(parameter);
this.parameterEstimationInitializationExpressions.remove(parameter);
this.parameterEstimationInitializationExpressionStrings.remove(parameter);
}
// Add new parameter references.
for (String parameter : parameterNames) {
if (this.referencedParameters.get(parameter) == null) {
this.referencedParameters.put(parameter, new HashSet<Node>());
}
Set<Node> nodes = this.referencedParameters.get(parameter);
nodes.add(node);
setSuitableParameterDistribution(parameter);
}
// Remove old node references.
List<Node> nodesToRemove = new LinkedList<>();
for (Node _node : this.referencedNodes.keySet()) {
Set<Node> nodes = this.referencedNodes.get(_node);
if (nodes.contains(node)) {
nodes.remove(node);
}
if (nodes.isEmpty()) {
nodesToRemove.add(_node);
}
}
for (Node _node : nodesToRemove) {
this.referencedNodes.remove(_node);
}
// Add new freeParameters.
for (String variableString : variableNames) {
Node _node = getNode(variableString);
if (this.referencedNodes.get(_node) == null) {
this.referencedNodes.put(_node, new HashSet<Node>());
}
for (String s : parentNames) {
if (s.equals(variableString)) {
Set<Node> nodes = this.referencedNodes.get(_node);
nodes.add(node);
}
}
}
// Finally, save the parsed expression and the original string that the user entered. No need to
// annoy
// the user by changing spacing.
nodeExpressions.put(node, expression);
nodeExpressionStrings.put(node, expressionString);
}
public GeneralizedSemPm(SemPm semPm) {
this(semPm.getGraph());
// Write down equations.
try {
List<Node> variableNodes = getVariableNodes();
for (int i = 0; i < variableNodes.size(); i++) {
Node node = variableNodes.get(i);
List<Node> parents = getVariableParents(node);
StringBuilder buf = new StringBuilder();
for (int j = 0; j < parents.size(); j++) {
if (!(variableNodes.contains(parents.get(j)))) {
continue;
}
Node parent = parents.get(j);
Parameter _parameter = semPm.getParameter(parent, node);
String parameter = _parameter.getName();
Set<Node> nodes = new HashSet<>();
nodes.add(node);
referencedParameters.put(parameter, nodes);
buf.append(parameter);
buf.append("*");
buf.append(parents.get(j).getName());
setParameterExpression(parameter, "Split(-1.5, -.5, .5, 1.5)");
setStartsWithParametersTemplate(parameter.substring(0, 1), "Split(-1.5, -.5, .5, 1.5)");
setStartsWithParametersEstimationInitializaationTemplate(
parameter.substring(0, 1), "Split(-1.5, -.5, .5, 1.5)");
if (j < parents.size() - 1) {
buf.append(" + ");
}
}
if (buf.toString().trim().length() != 0) {
buf.append(" + ");
}
buf.append(errorNodes.get(i));
setNodeExpression(node, buf.toString());
}
for (Node node : variableNodes) {
Parameter _parameter = semPm.getParameter(node, node);
String parameter = _parameter.getName();
String distributionFormula = "N(0," + parameter + ")";
setNodeExpression(getErrorNode(node), distributionFormula);
setParameterExpression(parameter, "U(0, 1)");
setStartsWithParametersTemplate(parameter.substring(0, 1), "U(0, 1)");
setStartsWithParametersEstimationInitializaationTemplate(
parameter.substring(0, 1), "U(0, 1)");
}
variableNames = new ArrayList<>();
for (Node _node : variableNodes) variableNames.add(_node.getName());
for (Node _node : errorNodes) variableNames.add(_node.getName());
} catch (ParseException e) {
throw new IllegalStateException("Parse error in constructing initial model.", e);
}
}