def MI_adaptive_soft(X, Y, hm_HypoTest):
Cx,X = np.unique(X, return_inverse = True)
Cy,Y = np.unique(Y, return_inverse = True)
X = X + 1
Y = Y + 1
m = len(Cx)
n = len(Cy)
joint_dist = np.ones([m,n]) * (1/(m*n))
mutual_info = 0
_,a = np.unique((np.column_stack((X, Y))),axis=0,return_counts=True)
if min(a) < 3:
mutual_info = mi(X,Y)
if m == 1 or n == 1:
mutual_info = np.inf
result = []
result.append(mutual_info)
result.append(joint_dist)
result.append(hm_HypoTest)
return result
result = []
result.append(mutual_info)
result.append(joint_dist)
result.append(hm_HypoTest)
return result
if min(a) > 10:
mutual_info = mi(X,Y)
if m == 1 or n == 1:
mutual_info = 0
result = []
result.append(mutual_info)
result.append(joint_dist)
result.append(hm_HypoTest)
return result
result = []
result.append(mutual_info)
result.append(joint_dist)
result.append(hm_HypoTest)
return result
if m == 1 or n == 1:
mutual_info = np.inf
#result = []
#result.append(mutual_info)
#result.append(joint_dist)
#result.append(hm_HypoTest)
return mutual_info, joint_dist, hm_HypoTest
#Estimate the joint probability mass by adaptive partitioning
joint_dist, hm_HypoTest, isUniform = jointPDFAdapPartition(X, Y, m, n, hm_HypoTest)
mutual_info = np.abs(get_MI_from_joint_distribution(joint_dist))
if isUniform or mutual_info <= 0.0000001:
mutual_info = np.inf
return mutual_info, joint_dist, hm_HypoTest
def GTest_I(X, Y):
sig_level_indep = 0.05
hm_x = len(np.unique(X))
hm_y = len(np.unique(Y))
hm_samples = X.size
g = 2 * hm_samples * mi(X, Y, 0)
p_val = 1 - chi2.cdf(g, (hm_x - 1) * (hm_y - 1))
if p_val < sig_level_indep:
Independency = 0 # reject the Null-hypothesis
else:
Independency = 1
return Independency
def sort_by_cmi(feat_indices, targets, cond_indices, data):
"""
Returns the indices found in 'feat_indices' in order of I(X;Y|Z), where Z
is the joint distribution described by data[cond_indices], X is the joint
distribution of data[feat_indices[i]], and Y is the joint distribution of
data[targets]. If Z is empty, then the result is I(X;Y)
"""
feats_to_cmi = dict()
if (cond_indices.size == 0):
for feature in feat_indices:
feats_to_cmi[feature] = mi(data[:, feature], targets)
else:
for feature in feat_indices:
feats_to_cmi[feature] = cmi(data[:, feature], targets,
joint(data[:, cond_indices]))
sorted_features = np.array(
sorted(feat_indices, key=lambda f: -feats_to_cmi[f]))
return sorted_features
def cmi(dataVector, targetVector, conditionVector, length=0):
if (conditionVector.size == 0):
return mi(dataVector, targetVector, 0)
if (len(conditionVector.shape) > 1 and conditionVector.shape[1] > 1):
conditionVector = joint(conditionVector)
cmi = 0
firstCondition = 0
secondCondition = 0
if length == 0:
length = dataVector.size
results = mergeArrays(targetVector, conditionVector, length)
mergedVector = results[1]
firstCondition = conditional_entropy(dataVector, conditionVector, length)
secondCondition = conditional_entropy(dataVector, mergedVector, length)
cmi = firstCondition - secondCondition
return cmi
def RecognizePC(targets, ADJt, data, THRESHOLD, NumTest):
MIs = []
NonPC = []
cutSetSize = 0
data_check = 1
#targets = data[:, T]
Sepset = [[]] * data.shape[1]
seperators = [[]] * data.shape[1]
#% Search
datasizeFlag = 0
while ADJt.size > cutSetSize:
for xind in range(0, ADJt.size): # for each x in ADJt
X = ADJt[xind]
if cutSetSize == 0:
NumTest = NumTest + 1
TEMP = mi(data[:, X], targets, 0)
MIs.append([TEMP]) #compute mutual information
#print("Vertex MI ",X,TEMP)
if TEMP <= THRESHOLD:
NonPC.append(X)
elif cutSetSize == 1:
Diffx = np.setdiff1d(ADJt, X)
C = list(combinations(Diffx, cutSetSize))
for sind in range(0, len(C)): # for each S in ADJT\x, size
S = np.array(list(C[sind]))
cmbVector = joint(data[:, S])
if data_check:
datasizeFlag = checkDataSize(data[:, X], targets,
cmbVector)
if datasizeFlag != 1:
NumTest = NumTest + 1
TEMP = cmi(data[:, X], targets, cmbVector, 0)
MIs.append([TEMP])
if TEMP <= THRESHOLD:
NonPC = set(NonPC).union(set([X]))
Sepset[X] = set(Sepset[X]).union(set(S))
break
else:
break
else: # set size > 1
Diffx = np.setdiff1d(ADJt, X)
C = list(combinations(Diffx, cutSetSize - 1))
midBreakflag = 0
for sind in range(0, len(C)): # for each S in ADJT\x, size
S = np.array(list(C[sind]))
RestSet = np.setdiff1d(Diffx, S)
for addind in range(0, RestSet.size):
col = set(S).union(set([RestSet[addind]]))
cmbVector = joint(data[:, np.array(list(col))])
if data_check:
datasizeFlag = checkDataSize(
data[:, X], targets, cmbVector)
if datasizeFlag != 1:
NumTest = NumTest + 1
TEMP = cmi(data[:, X], targets, cmbVector, 0)
MIs.append([TEMP])
if TEMP <= THRESHOLD:
NonPC = set(NonPC).union(set([X]))
# Line has an error
Sepset[X] = set(Sepset[X]).union(
set(S), set([RestSet[addind]]))
midBreakflag = 1
break
else:
break
if midBreakflag == 1:
break
if len(NonPC) > 0:
ADJt = np.setdiff1d(ADJt, np.array(list(NonPC)))
cutSetSize = cutSetSize + 1
# print("NonPC")
# print(NonPC)
# print(len(NonPC))
NonPC = []
elif datasizeFlag == 1:
break
else:
cutSetSize = cutSetSize + 1
ADJ = ADJt
result = []
result.append(ADJ)
result.append(Sepset)
result.append(NumTest)
result.append(cutSetSize)
result.append(MIs)
return result