// Build a directed tree from a root
private void treeify(int root, int[][] paPoly, int[][] paTemp) throws Exception {
int children[] = new int[] {};
for (int j = 0; j < paPoly[root].length; j++) {
if (paPoly[root][j] != 0 && !visited[j]) {
visited[j] = true;
children = A.append(children, j);
if (paPoly[root][j] != 3) paTemp[j] = A.append(paTemp[j], root);
}
}
// go through again
for (int child : children) treeify(child, paPoly, paTemp);
}
// Rank the labels for the chain order
private void rankLabel(int root, int[][] paPoly, int[] rank) throws Exception {
if (!visited[root]) {
int[] parents = new int[] {};
int[] children = new int[] {};
for (int j = 0; j < rank.length; j++) {
if (paPoly[root][j] == 3) {
rank[j] = rank[root] - 1;
parents = A.append(parents, j);
}
if (paPoly[root][j] == 2) {
rank[j] = rank[root] + 1;
children = A.append(children, j);
}
}
visited[root] = true;
for (int parent : parents) rankLabel(parent, paPoly, rank);
for (int child : children) rankLabel(child, paPoly, rank);
}
}
// Learning of the tree skeleton (paTree)
protected int[][] skeleton(double[][] CD) throws Exception {
CD = M.multiply(CD, -1);
EdgeWeightedGraph G = new EdgeWeightedGraph(L);
for (int i = 0; i < L; i++) {
for (int j = i + 1; j < L; j++) {
Edge e = new Edge(i, j, CD[i][j]);
G.addEdge(e);
}
}
KruskalMST mst = new KruskalMST(G);
int[][] paTree = new int[L][0];
for (int j = 0; j < L; j++) paTree[j] = new int[] {};
for (Edge e : mst.edges()) {
int j = e.either();
int k = e.other(j);
paTree[j] = A.append(paTree[j], k);
paTree[k] = A.append(paTree[k], j);
}
return paTree;
}
/**
* Transform.
*
* @param D original Instances
* @param c to be the class Attribute
* @param pa_c the parent indices of c
* @return new Instances T
*/
public static Instances transform(Instances D, int c, int pa_c[]) throws Exception {
int L = D.classIndex();
int keep[] = A.append(pa_c, c); // keep all parents and self!
Arrays.sort(keep);
int remv[] = A.invert(keep, L); // i.e., remove the rest < L
Arrays.sort(remv);
Instances T = F.remove(new Instances(D), remv, false);
int map[] = new int[L];
for (int j = 0; j < L; j++) {
map[j] = Arrays.binarySearch(keep, j);
}
T.setClassIndex(map[c]);
return T;
}
/**
* Transform - transform dataset D for this node. this.j defines the current node index, e.g., 3
* this.paY[] defines parents, e.g., [1,4] we should remove the rest, e.g., [0,2,5,...,L-1]
*
* @return dataset we should remove all variables from D EXCEPT current node, and parents.
*/
public Instances transform(Instances D) throws Exception {
int L = D.classIndex();
d = D.numAttributes() - L;
int keep[] = A.append(this.paY, j); // keep all parents and self!
Arrays.sort(keep);
int remv[] = A.invert(keep, L); // i.e., remove the rest < L
Arrays.sort(remv);
map = new int[L];
for (int j = 0; j < L; j++) {
map[j] = Arrays.binarySearch(keep, j);
}
Instances D_ = F.remove(new Instances(D), remv, false);
D_.setClassIndex(map[this.j]);
return D_;
}
// Calculation of conditional dependence between labels given the observation of instances
protected double[][] conDepMatrix(Instances[] newData) throws Exception {
int L = newData[0].classIndex();
CNode[][] miNodes = new CNode[L][];
int[] paNode;
Classifier model = new Logistic();
double MI[][] = new double[L][L];
// n-fold CV for calculation of MI matrix
for (int i = 0; i < numFolds; i++) {
Instances[] D_train = new Instances[L];
Instances[] D_test = new Instances[L];
for (int j = 0; j < L; j++) {
D_train[j] = newData[j].trainCV(numFolds, i);
D_test[j] = newData[j].testCV(numFolds, i);
}
// train L*(L+1)/2 logistic classifiers for calculating conditional probability.
for (int j = 0; j < L; j++) {
miNodes[j] = new CNode[L - j];
paNode = new int[] {};
for (int k = j; k < L; k++) {
if (k != j) paNode = A.append(paNode, k);
miNodes[j][k - j] = new CNode(j, null, paNode);
miNodes[j][k - j].build(D_train[j], model);
if (k != j) paNode = A.delete(paNode, 0);
}
}
// calculate the conditional mutual information
for (int j = 0; j < L; j++)
for (int k = j + 1; k < L; k++) MI[j][k] = conMI(D_test[j], D_test[k], miNodes, j, k);
MI = addMatrix(MI, MI);
}
return MI;
}
// Build a polytree on the tree
protected int[][] polyTree(Instances D, Instances[] newD) throws Exception {
L = (D == null) ? newD[0].classIndex() : D.classIndex();
CD = new double[L][L];
numVisited = 0;
int root = 0;
int[][] pa = new int[L][0];
visited = new boolean[L];
flagCB = new boolean[L];
Arrays.fill(visited, false);
Arrays.fill(flagCB, false);
if (depMode) {
// Calculate the conditional MI matrix
if (newD == null) CD = conDepMatrix(D);
if (newD != null) CD = conDepMatrix(newD);
} else {
// Calculate the marginal normalized MI matrix
CD = StatUtilsPro.NormMargDep(D);
}
// Build the tree skeleton
int[][] paTree = skeleton(CD);
// Find the causal basins
int[][] paPoly = new int[L][L];
causalBasin(root, paTree, paPoly);
// If causal basin can't cover all labels, build a directed tree (paTemp)
int[][] paTemp = new int[L][0];
root = -1;
for (int j = 0; j < L; j++) {
for (int k = j; k < L; k++) {
if (paPoly[j][k] == 1) {
root = j;
Arrays.fill(visited, false);
visited[root] = true;
treeify(root, paPoly, paTemp);
break;
}
}
if (root != -1) break;
}
// Save the parents of every node in the polytree (pa)
for (int j = 0; j < L; j++) {
for (int k = j; k < L; k++) {
if (paPoly[j][k] == 3) pa[j] = A.append(pa[j], k);
if (paPoly[j][k] == 2) pa[k] = A.append(pa[k], j);
}
}
for (int j = 0; j < L; j++) {
if (pa[j].length < 1) {
for (int v : paTemp[j]) {
pa[j] = A.append(pa[j], v);
paPoly[j][v] = 3;
paPoly[v][j] = 2;
}
}
}
// Rank the labels in the polytree (rank)
root = 0;
int[] rank = new int[L];
Arrays.fill(rank, 0);
Arrays.fill(visited, false);
rankLabel(root, paPoly, rank);
chainOrder = Utils.sort(rank);
// Enhance the polytree
int[] temp = new int[] {};
double thCD = 0.0005;
for (int j : chainOrder) {
for (int k : temp) {
if (paPoly[j][k] != 3) {
if (j < k && CD[j][k] > thCD) pa[j] = A.append(pa[j], k);
if (j > k && CD[k][j] > thCD) pa[j] = A.append(pa[j], k);
}
}
temp = A.append(temp, j);
}
return pa;
}
private void zeroMI(int root, int[][] paTree, int[][] paPoly) throws Exception {
// Calculation the threshold
double min = 1.0;
for (int j : paTree[root]) {
if (root < j) min = CD[root][j] < min ? CD[root][j] : min;
else min = CD[j][root] < min ? CD[j][root] : min;
}
double miThreshold = para1 * min;
// Find all the candidates parents by thresholding
int[] paTemp = new int[] {};
boolean[] selected = new boolean[paPoly[0].length];
Arrays.fill(selected, false);
for (int j : paTree[root]) {
for (int k : paTree[root]) {
if (j < k) {
if (paPoly[root][j] != 2 && paPoly[root][k] != 2) {
if (CD[j][k] < miThreshold) {
if (!selected[j]) {
paTemp = A.append(paTemp, j);
selected[j] = true;
}
if (!selected[k]) {
paTemp = A.append(paTemp, k);
selected[k] = true;
}
}
}
}
}
}
// 1 if root is a multi-parent node, save its direct parents and children if any
if (paTemp.length > 1) {
int maxN = para2; // set the maximum number of parents
double[] DepScore = new double[paTemp.length];
for (int j = 0; j < paTemp.length; j++) {
for (int k : paTemp) {
if (paTemp[j] < k) DepScore[j] = DepScore[j] + CD[paTemp[j]][k];
else DepScore[j] = DepScore[j] + CD[k][paTemp[j]];
}
}
double[] copyDepScore = DepScore.clone();
Arrays.sort(copyDepScore);
// 1.1 |pa(root)| exceeds the maxN, remove some parents from pa(root)
if (paTemp.length > maxN) {
for (int j = 0; j < maxN; j++) {
for (int k = 0; k < DepScore.length; k++) {
if (copyDepScore[j] == DepScore[k]) {
paPoly[root][paTemp[k]] = 3;
paPoly[paTemp[k]][root] = 2;
flagCB[root] = true;
}
}
}
} else {
// 1.2 otherwise (pa(root) is small enough), save the pa(root)
for (int j : paTemp) {
paPoly[root][j] = 3;
paPoly[j][root] = 2;
flagCB[root] = true;
}
}
// save the non-parent nodes as child nodes
for (int j : paTree[root]) {
if (paPoly[root][j] != 3) {
paPoly[root][j] = 2;
paPoly[j][root] = 3;
flagCB[j] = true;
}
}
visited[root] = true;
numVisited++;
} else if (flagCB[root]) { // 2 if CB exists for root, build it following causal flows
for (int j : paTree[root]) {
if (paPoly[root][j] != 3) {
paPoly[root][j] = 2;
paPoly[j][root] = 3;
flagCB[j] = true;
}
}
visited[root] = true;
numVisited++;
} else { // 3 if CB doesn't exist for root, assign undirected edges
for (int j : paTree[root]) {
if (paPoly[root][j] == 0) paPoly[root][j] = 1;
}
visited[root] = true;
numVisited++;
}
}