/**
* 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);
}
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);
}
/** Meek's rule R3. If a--b, a--c, a--d, c-->b, c-->b, then orient a-->b. */
public static boolean meekR3(Graph graph, Knowledge knowledge) {
List<Node> nodes = graph.getNodes();
boolean changed = false;
for (Node a : nodes) {
List<Node> adjacentNodes = graph.getAdjacentNodes(a);
if (adjacentNodes.size() < 3) {
continue;
}
for (Node b : adjacentNodes) {
List<Node> otherAdjacents = new LinkedList<Node>(adjacentNodes);
otherAdjacents.remove(b);
if (!graph.isUndirectedFromTo(a, b)) {
continue;
}
ChoiceGenerator cg = new ChoiceGenerator(otherAdjacents.size(), 2);
int[] combination;
while ((combination = cg.next()) != null) {
Node c = otherAdjacents.get(combination[0]);
Node d = otherAdjacents.get(combination[1]);
if (graph.isAdjacentTo(c, d)) {
continue;
}
if (!graph.isUndirectedFromTo(a, c)) {
continue;
}
if (!graph.isUndirectedFromTo(a, d)) {
continue;
}
if (graph.isDirectedFromTo(c, b) && graph.isDirectedFromTo(d, b)) {
if (isArrowpointAllowed(a, b, knowledge)) {
graph.setEndpoint(a, b, Endpoint.ARROW);
TetradLogger.getInstance()
.edgeOriented(SearchLogUtils.edgeOrientedMsg("Meek R3", graph.getEdge(a, b)));
changed = true;
break;
}
}
}
}
}
return changed;
}
/** Tests to see if d separation facts are symmetric. */
public void testDSeparation() {
EdgeListGraphSingleConnections graph =
new EdgeListGraphSingleConnections(
new Dag(GraphUtils.randomGraph(7, 0, 7, 30, 15, 15, true)));
System.out.println(graph);
List<Node> nodes = graph.getNodes();
int depth = -1;
for (int i = 0; i < nodes.size(); i++) {
for (int j = i + 1; j < nodes.size(); j++) {
Node x = nodes.get(i);
Node y = nodes.get(j);
List<Node> theRest = new ArrayList<Node>(nodes);
theRest.remove(x);
theRest.remove(y);
DepthChoiceGenerator gen = new DepthChoiceGenerator(theRest.size(), depth);
int[] choice;
while ((choice = gen.next()) != null) {
List<Node> z = new LinkedList<Node>();
for (int k = 0; k < choice.length; k++) {
z.add(theRest.get(choice[k]));
}
if (graph.isDSeparatedFrom(x, y, z) != graph.isDSeparatedFrom(y, x, z)) {
fail(
SearchLogUtils.independenceFact(x, y, z)
+ " should have same d-sep result as "
+ SearchLogUtils.independenceFact(y, x, z));
}
}
}
}
}
private void resolveOneEdgeMax(Graph graph, Node x, Node y, boolean strong, Graph oldGraph) {
if (RandomUtil.getInstance().nextDouble() > 0.5) {
Node temp = x;
x = y;
y = temp;
}
TetradLogger.getInstance().log("info", "\nEDGE " + x + " --- " + y);
SortedMap<Double, String> scoreReports = new TreeMap<Double, String>();
List<Node> neighborsx = graph.getAdjacentNodes(x);
neighborsx.remove(y);
double max = Double.NEGATIVE_INFINITY;
boolean left = false;
boolean right = false;
DepthChoiceGenerator genx = new DepthChoiceGenerator(neighborsx.size(), neighborsx.size());
int[] choicex;
while ((choicex = genx.next()) != null) {
List<Node> condxMinus = GraphUtils.asList(choicex, neighborsx);
List<Node> condxPlus = new ArrayList<Node>(condxMinus);
condxPlus.add(y);
double xPlus = score(x, condxPlus);
double xMinus = score(x, condxMinus);
List<Node> neighborsy = graph.getAdjacentNodes(y);
neighborsy.remove(x);
DepthChoiceGenerator geny = new DepthChoiceGenerator(neighborsy.size(), neighborsy.size());
int[] choicey;
while ((choicey = geny.next()) != null) {
List<Node> condyMinus = GraphUtils.asList(choicey, neighborsy);
// List<Node> parentsY = oldGraph.getParents(y);
// parentsY.remove(x);
// if (!condyMinus.containsAll(parentsY)) {
// continue;
// }
List<Node> condyPlus = new ArrayList<Node>(condyMinus);
condyPlus.add(x);
double yPlus = score(y, condyPlus);
double yMinus = score(y, condyMinus);
// Checking them all at once is expensive but avoids lexical ordering problems in the
// algorithm.
if (normal(y, condyPlus)
|| normal(x, condxMinus)
|| normal(x, condxPlus)
|| normal(y, condyMinus)) {
continue;
}
double delta = 0.0;
if (strong) {
if (yPlus <= xPlus + delta && xMinus <= yMinus + delta) {
double score = combinedScore(xPlus, yMinus);
if (yPlus <= yMinus + delta && xMinus <= xPlus + delta) {
StringBuilder builder = new StringBuilder();
builder.append("\nStrong " + y + "->" + x + " " + score);
builder.append("\n Parents(" + x + ") = " + condxMinus);
builder.append("\n Parents(" + y + ") = " + condyMinus);
scoreReports.put(-score, builder.toString());
if (score > max) {
max = score;
left = true;
right = false;
}
} else {
StringBuilder builder = new StringBuilder();
builder.append("\nNo directed edge " + x + "--" + y + " " + score);
builder.append("\n Parents(" + x + ") = " + condxMinus);
builder.append("\n Parents(" + y + ") = " + condyMinus);
scoreReports.put(-score, builder.toString());
}
} else if (xPlus <= yPlus + delta && yMinus <= xMinus + delta) {
double score = combinedScore(yPlus, xMinus);
if (yMinus <= yPlus + delta && xPlus <= xMinus + delta) {
StringBuilder builder = new StringBuilder();
builder.append("\nStrong " + x + "->" + y + " " + score);
builder.append("\n Parents(" + x + ") = " + condxMinus);
builder.append("\n Parents(" + y + ") = " + condyMinus);
scoreReports.put(-score, builder.toString());
if (score > max) {
max = score;
left = false;
right = true;
}
} else {
StringBuilder builder = new StringBuilder();
builder.append("\nNo directed edge " + x + "--" + y + " " + score);
builder.append("\n Parents(" + x + ") = " + condxMinus);
builder.append("\n Parents(" + y + ") = " + condyMinus);
scoreReports.put(-score, builder.toString());
}
} else if (yPlus <= xPlus + delta && yMinus <= xMinus + delta) {
double score = combinedScore(yPlus, xMinus);
StringBuilder builder = new StringBuilder();
builder.append("\nNo directed edge " + x + "--" + y + " " + score);
builder.append("\n Parents(" + x + ") = " + condxMinus);
builder.append("\n Parents(" + y + ") = " + condyMinus);
scoreReports.put(-score, builder.toString());
} else if (xPlus <= yPlus + delta && xMinus <= yMinus + delta) {
double score = combinedScore(yPlus, xMinus);
StringBuilder builder = new StringBuilder();
builder.append("\nNo directed edge " + x + "--" + y + " " + score);
builder.append("\n Parents(" + x + ") = " + condxMinus);
builder.append("\n Parents(" + y + ") = " + condyMinus);
scoreReports.put(-score, builder.toString());
}
} else {
if (yPlus <= xPlus + delta && xMinus <= yMinus + delta) {
double score = combinedScore(xPlus, yMinus);
StringBuilder builder = new StringBuilder();
builder.append("\nWeak " + y + "->" + x + " " + score);
builder.append("\n Parents(" + x + ") = " + condxMinus);
builder.append("\n Parents(" + y + ") = " + condyMinus);
scoreReports.put(-score, builder.toString());
if (score > max) {
max = score;
left = true;
right = false;
}
} else if (xPlus <= yPlus + delta && yMinus <= xMinus + delta) {
double score = combinedScore(yPlus, xMinus);
StringBuilder builder = new StringBuilder();
builder.append("\nWeak " + x + "->" + y + " " + score);
builder.append("\n Parents(" + x + ") = " + condxMinus);
builder.append("\n Parents(" + y + ") = " + condyMinus);
scoreReports.put(-score, builder.toString());
if (score > max) {
max = score;
left = false;
right = true;
}
} else if (yPlus <= xPlus + delta && yMinus <= xMinus + delta) {
double score = combinedScore(yPlus, xMinus);
StringBuilder builder = new StringBuilder();
builder.append("\nNo directed edge " + x + "--" + y + " " + score);
builder.append("\n Parents(" + x + ") = " + condxMinus);
builder.append("\n Parents(" + y + ") = " + condyMinus);
scoreReports.put(-score, builder.toString());
} else if (xPlus <= yPlus + delta && xMinus <= yMinus + delta) {
double score = combinedScore(yPlus, xMinus);
StringBuilder builder = new StringBuilder();
builder.append("\nNo directed edge " + x + "--" + y + " " + score);
builder.append("\n Parents(" + x + ") = " + condxMinus);
builder.append("\n Parents(" + y + ") = " + condyMinus);
scoreReports.put(-score, builder.toString());
}
}
}
}
for (double score : scoreReports.keySet()) {
TetradLogger.getInstance().log("info", scoreReports.get(score));
}
graph.removeEdges(x, y);
if (left) {
graph.addDirectedEdge(y, x);
}
if (right) {
graph.addDirectedEdge(x, y);
}
if (!graph.isAdjacentTo(x, y)) {
graph.addUndirectedEdge(x, y);
}
}
////////////////////////////////////////////
// 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);
}
// 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;
}