Fix GIN

Author: zhi-yi-huang

causallearn/search/HiddenCausal/GIN/GIN.py

@@ -5,18 +5,154 @@
     From DMIRLab: https://dmir.gdut.edu.cn/
 '''
 
+import random
 from collections import deque
 from itertools import combinations
 
 import numpy as np
+from scipy.stats import chi2
 
 from causallearn.graph.GeneralGraph import GeneralGraph
 from causallearn.graph.GraphNode import GraphNode
 from causallearn.graph.NodeType import NodeType
+from causallearn.graph.Edge import Edge
+from causallearn.graph.Endpoint import Endpoint
 from causallearn.search.FCMBased.lingam.hsic import hsic_test_gamma
+from causallearn.utils.cit import kci
 
 
-def GIN(data):
+def fisher_test(pvals):
+    pvals = [pval if pval >= 1e-5 else 1e-5 for pval in pvals]
+    return min(pvals)
+    # fisher_stat = -2.0 * np.sum(np.log(pvals))
+    # return 1 - chi2.cdf(fisher_stat, 2 * len(pvals))
+
+
+def GIN(data, indep_test=kci, alpha=0.05):
+    '''
+    Learning causal structure of Latent Variables for Linear Non-Gaussian Latent Variable Model
+    with Generalized Independent Noise Condition
+
+    Parameters
+    ----------
+    data : numpy ndarray
+           data set
+    indep_test : callable, default=kci
+        the function of the independence test being used
+    alpha : float, default=0.05
+        desired significance level of independence tests (p_value) in (0,1)
+    Returns
+    -------
+    G : general graph
+        causal graph
+    K : list
+        causal order
+    '''
+    n = data.shape[1]
+    cov = np.cov(data.T)
+
+    var_set = set(range(n))
+    cluster_size = 2
+    clusters_list = []
+    while cluster_size < len(var_set):
+        tmp_clusters_list = []
+        for cluster in combinations(var_set, cluster_size):
+            remain_var_set = var_set - set(cluster)
+            e = cal_e_with_gin(data, cov, list(cluster), list(remain_var_set))
+            pvals = []
+            tmp_data = np.concatenate([data[:, list(remain_var_set)], e.reshape(-1, 1)], axis=1)
+            for z in range(len(remain_var_set)):
+                pvals.append(indep_test(tmp_data, z, - 1))
+            fisher_pval = fisher_test(pvals)
+            if fisher_pval >= alpha:
+                tmp_clusters_list.append(cluster)
+        tmp_clusters_list = merge_overlaping_cluster(tmp_clusters_list)
+        clusters_list = clusters_list + tmp_clusters_list
+        for cluster in tmp_clusters_list:
+            var_set -= set(cluster)
+        cluster_size += 1
+
+    K = []
+    updated = True
+    while updated:
+        updated = False
+        X = []
+        Z = []
+        for cluster_k in K:
+            cluster_k1, cluster_k2 = array_split(cluster_k, 2)
+            X += cluster_k1
+            Z += cluster_k2
+
+        for i, cluster_i in enumerate(clusters_list):
+            is_root = True
+            random.shuffle(cluster_i)
+            cluster_i1, cluster_i2 = array_split(cluster_i, 2)
+            for j, cluster_j in enumerate(clusters_list):
+                if i == j:
+                    continue
+                random.shuffle(cluster_j)
+                cluster_j1, cluster_j2 = array_split(cluster_j, 2)
+                e = cal_e_with_gin(data, cov, X + cluster_i1 + cluster_j1, Z + cluster_i2)
+                pvals = []
+                tmp_data = np.concatenate([data[:, Z + cluster_i2], e.reshape(-1, 1)], axis=1)
+                for z in range(len(Z + cluster_i2)):
+                    pvals.append(indep_test(tmp_data, z, - 1))
+                fisher_pval = fisher_test(pvals)
+                if fisher_pval < alpha:
+                    is_root = False
+                    break
+            if is_root:
+                K.append(cluster_i)
+                clusters_list.remove(cluster_i)
+                updated = True
+                break
+
+    G = GeneralGraph([])
+    for var in var_set:
+        o_node = GraphNode(f"X{var + 1}")
+        G.add_node(o_node)
+
+    latent_id = 1
+    l_nodes = []
+
+    for cluster in K:
+        l_node = GraphNode(f"L{latent_id}")
+        l_node.set_node_type(NodeType.LATENT)
+        G.add_node(l_node)
+        for l in l_nodes:
+            G.add_directed_edge(l, l_node)
+        l_nodes.append(l_node)
+
+        for o in cluster:
+            o_node = GraphNode(f"X{o + 1}")
+            G.add_node(o_node)
+            G.add_directed_edge(l_node, o_node)
+        latent_id += 1
+
+    undirected_l_nodes = []
+
+    for cluster in clusters_list:
+        l_node = GraphNode(f"L{latent_id}")
+        l_node.set_node_type(NodeType.LATENT)
+        G.add_node(l_node)
+        for l in l_nodes:
+            G.add_directed_edge(l, l_node)
+
+        for l in undirected_l_nodes:
+            G.add_edge(Edge(l, l_node, Endpoint.TAIL, Endpoint.TAIL))
+
+        undirected_l_nodes.append(l_node)
+
+        for o in cluster:
+            o_node = GraphNode(f"X{o + 1}")
+            G.add_node(o_node)
+            G.add_directed_edge(l_node, o_node)
+        latent_id += 1
+
+    return G, K
+
+
+def GIN_MI(data):
     '''
     Learning causal structure of Latent Variables for Linear Non-Gaussian Latent Variable Model
     with Generalized Independent Noise Condition
@@ -81,6 +217,13 @@ def GIN(data):
     return G, K
 
 
+def cal_e_with_gin(data, cov, X, Z):
+    cov_m = cov[np.ix_(Z, X)]
+    _, _, v = np.linalg.svd(cov_m)
+    omega = v.T[:, -1]
+    return np.dot(omega, data[:, X].T)
+
+
 def cal_dep_for_gin(data, cov, X, Z):
     '''
     Calculate the statistics of dependence via Generalized Independent Noise Condition
@@ -96,10 +239,8 @@ def cal_dep_for_gin(data, cov, X, Z):
     -------
     sta : test statistic
     '''
-    cov_m = cov[np.ix_(Z, X)]
-    _, _, v = np.linalg.svd(cov_m)
-    omega = v.T[:, -1]
-    e_xz = np.dot(omega, data[:, X].T)
+
+    e_xz = cal_e_with_gin(data, cov, X, Z)
 
     sta = 0
     for i in Z:
@@ -160,6 +301,8 @@ def _get_all_elements(S):
 # merging cluster
 def merge_overlaping_cluster(cluster_list):
     v_labels = _get_all_elements(cluster_list)
+    if len(v_labels) == 0:
+        return []
     cluster_dict = {i: -1 for i in v_labels}
     cluster_b = {i: [] for i in v_labels}
     cluster_len = 0
@@ -197,3 +340,20 @@ def merge_overlaping_cluster(cluster_list):
         cluster[cluster_dict[i]].append(i)
 
     return cluster
+
+
+def array_split(x, k):
+    x_len = len(x)
+    # div_points = []
+    sub_arys = []
+    start = 0
+    section_len = x_len // k
+    extra = x_len % k
+    for i in range(extra):
+        sub_arys.append(x[start:start + section_len + 1])
+        start = start + section_len + 1
+
+    for i in range(k - extra):
+        sub_arys.append(x[start:start + section_len])
+        start = start + section_len
+    return sub_arys

tests/TestGIN.py

@@ -1,3 +1,4 @@
+import random
 import sys
 
 sys.path.append("")
@@ -45,3 +46,26 @@ def test_case2(self):
         data = (data - np.mean(data, axis=0)) / np.std(data, axis=0)
         g, k = GIN(data)
         print(g, k)
+
+    def test_case3(self):
+        sample_size = 1000
+        random.seed(42)
+        np.random.seed(42)
+        L1 = np.random.uniform(-1, 1, size=sample_size) ** 5
+        L2 = np.random.uniform(0.5, 2.0) * L1 + np.random.uniform(-1, 1, size=sample_size) ** 5
+        L3 = np.random.uniform(0.5, 2.0) * L1 + np.random.uniform(0.5, 2.0) * L2 + np.random.uniform(-1, 1, size=sample_size) ** 5
+        L4 = np.random.uniform(0.5, 2.0) * L1 + np.random.uniform(0.5, 2.0) * L2 + np.random.uniform(0.5, 2.0) * L3 + np.random.uniform(-1, 1, size=sample_size) ** 5
+
+        X1 = np.random.uniform(0.5, 2.0) * L1 + np.random.uniform(0.5, 2.0) * L2 + np.random.uniform(-1, 1, size=sample_size) ** 5
+        X2 = np.random.uniform(0.5, 2.0) * L1 + np.random.uniform(0.5, 2.0) * L2 + np.random.uniform(-1, 1, size=sample_size) ** 5
+        X3 = np.random.uniform(0.5, 2.0) * L1 + np.random.uniform(0.5, 2.0) * L2 + np.random.uniform(-1, 1, size=sample_size) ** 5
+        X4 = np.random.uniform(0.5, 2.0) * L1 + np.random.uniform(0.5, 2.0) * L2 + np.random.uniform(-1, 1, size=sample_size) ** 5
+        X5 = np.random.uniform(0.5, 2.0) * L3 + np.random.uniform(-1, 1, size=sample_size) ** 5
+        X6 = np.random.uniform(0.5, 2.0) * L3 + np.random.uniform(-1, 1, size=sample_size) ** 5
+        X7 = np.random.uniform(0.5, 2.0) * L4 + np.random.uniform(-1, 1, size=sample_size) ** 5
+        X8 = np.random.uniform(0.5, 2.0) * L4 + np.random.uniform(-1, 1, size=sample_size) ** 5
+
+        data = np.array([X1, X2, X3, X4, X5, X6, X7, X8]).T
+        data = (data - np.mean(data, axis=0)) / np.std(data, axis=0)
+        g, k = GIN(data)
+        print(g, k)