def isCondIndMI(self, var1, var2, var3):
d1 = self.data.getSeries(var1)
d2 = self.data.getSeries(var2)
d3 = self.data.getSeries(var3)
# d1 = self.standardize(d1)
# d2 = self.standardize(d2)
# d3 = self.standardize(d3)
p1 = self.mi_prepare(d1)
p2 = self.mi_prepare(d2)
p3 = self.mi_prepare(d3)
cmi = ee.cmi(p1, p2, p3, k=3)
e1 = self.getEntropy(var1)
e2 = self.getEntropy(var2)
e3 = self.getEntropy(var3)
normCmi = cmi / (e1 * e2 * e3)**(1 / 3.0)
result = normCmi < miCondIndThreshold
Dprint('CI: ', var1, '_||_', var2, '|', var3, '=', result, normCmi)
return result
def isWinning(feature_col, coalition, rows, threshold=0.50):
''' Checks if union of the feature and coalitions leads to win
A feature is winning if it's interdependent on atleast half of the members in the coalition.
The interdependence is measured using conditional mutual information.
'''
total_dependence = 0
x = feature_col.reshape(-1, 1).tolist()
if len(coalition) == 1:
y = rows[:, [coalition[0]]].tolist()
return ee.mi(x, y) >= threshold
for i in range(0, len(coalition)):
y = rows[:, [coalition[i]]].tolist()
z = rows[:, coalition[:i] + coalition[i + 1:]].tolist()
if ee.cmi(x, y, z) >= threshold:
total_dependence = total_dependence + 1
return float(total_dependence) / float(len(coalition)) >= 0.5
trueent += 0.5 * (2 + log(4. * pi * pi * det(
[[cov[0][0], cov[0][2]], [cov[2][0], cov[2][2]]]))) # xz sub
trueent += 0.5 * (2 + log(4. * pi * pi * det(
[[cov[1][1], cov[1][2]], [cov[2][1], cov[2][2]]]))) # yz sub
print('true CMI(x:y|x)', trueent / log(2))
ent = []
err = []
for NN in Ntry:
tempent = []
for j in range(nsamples):
points = nr.multivariate_normal(mean, cov, NN)
x = [point[:1] for point in points]
y = [point[1:2] for point in points]
z = [point[2:] for point in points]
tempent.append(ee.cmi(x, y, z))
tempent.sort()
tempmean = np.mean(tempent)
ent.append(tempmean)
err.append((tempmean - tempent[samplo], tempent[samphi] - tempmean))
print('samples used', Ntry)
print('estimated CMI', ent)
print('95% conf int. (a, b) means (mean - a, mean + b)is interval\n', err)
# MUTUAL INFORMATION
print('Mutual Information')
trueent = 0.5 * (1 + log(2. * pi * cov[0][0])) # x sub
trueent += 0.5 * (1 + log(2. * pi * cov[1][1])) # y sub
trueent += -0.5 * (2 + log(4. * pi * pi * det(
trueent = -0.5*(3+log(8.*pi*pi*pi*det(cov)))
trueent += -0.5*(1+log(2.*pi*cov[2][2])) #z sub
trueent += 0.5*(2+log(4.*pi*pi*det([[cov[0][0],cov[0][2]],[cov[2][0],cov[2][2]]] ))) #xz sub
trueent += 0.5*(2+log(4.*pi*pi*det([[cov[1][1],cov[1][2]],[cov[2][1],cov[2][2]]] ))) #yz sub
print 'true CMI(x:y|x)', trueent/log(2)
ent = []
err = []
for NN in Ntry:
tempent = []
for j in range(nsamples):
points = nr.multivariate_normal(mean,cov,NN)
x = [point[:1] for point in points]
y = [point[1:2] for point in points]
z = [point[2:] for point in points]
tempent.append(ee.cmi(x,y,z))
tempent.sort()
tempmean = np.mean(tempent)
ent.append(tempmean)
err.append((tempmean - tempent[samplo],tempent[samphi]-tempmean))
print 'samples used',Ntry
print 'estimated CMI',ent
print '95% conf int. (a,b) means (mean-a,mean+b)is interval\n',err
## MUTUAL INFORMATION
print 'Mutual Information'
trueent = 0.5*(1+log(2.*pi*cov[0][0])) #x sub
trueent += 0.5*(1+log(2.*pi*cov[1][1])) #y sub
trueent += -0.5*(2+log(4.*pi*pi*det([[cov[0][0],cov[0][1]],[cov[1][0],cov[1][1]]] ))) #xz sub