def generate_dirichlet_data(ndag, size):
order = ndag.getTopologicalOrder()
copulas = []
for k in range(order.getSize()):
d = 1 + ndag.getParents(k).getSize()
copulas.append(ot.Dirichlet([(1.0+k)/(d+1) for k in range(d+1)]).getCopula())
cbn = otagr.ContinuousBayesianNetwork(ndag, [ot.Uniform(0., 1.)]*ndag.getSize(), copulas)
sample = cbn.getSample(size)
return sample
def generate_dirichlet_data(ndag, size):
order = ndag.getTopologicalOrder()
jointDistributions = []
for k in range(order.getSize()):
d = 1 + ndag.getParents(k).getSize()
jointDistributions.append(
ot.Dirichlet([(1.0 + k) / (d + 1)
for k in range(d + 1)]).getCopula())
copula = otagr.ContinuousBayesianNetwork(ndag, jointDistributions)
sample = copula.getSample(size)
return sample
def generate_gaussian_data(ndag, size, r=0.8):
order = ndag.getTopologicalOrder()
copulas = []
for k in range(order.getSize()):
d = 1 + ndag.getParents(k).getSize()
R = ot.CorrelationMatrix(d)
for i in range(d):
for j in range(i):
R[i, j] = r
copulas.append(ot.NormalCopula(R))
cbn = otagr.ContinuousBayesianNetwork(ndag, [ot.Uniform(0., 1.)]*ndag.getSize(), copulas)
sample = cbn.getSample(size)
return sample
def generate_student_data(ndag, size, r=0.8):
order = ndag.getTopologicalOrder()
jointDistributions = []
for k in range(order.getSize()):
d = 1 + ndag.getParents(k).getSize()
R = ot.CorrelationMatrix(d)
for i in range(d):
for j in range(i):
R[i, j] = r
jointDistributions.append(
ot.Student(5.0, [0.0] * d, [1.0] * d, R).getCopula())
copula = otagr.ContinuousBayesianNetwork(ndag, jointDistributions)
sample = copula.getSample(size)
return sample
marginals = [ot.Uniform(0.0, 1.0) for i in range(order.getSize())]
copulas = list()
for i in range(order.getSize()):
d = 1 + ndag.getParents(i).getSize()
print("i=", i, ", d=", d)
if d == 1:
copulas.append(ot.IndependentCopula(1))
else:
R = ot.CorrelationMatrix(d)
for i in range(d):
for j in range(i):
R[i, j] = 0.5 / d
copulas.append(
ot.Student(5.0, [0.0] * d, [1.0] * d, R).getCopula())
cbn = otagrum.ContinuousBayesianNetwork(ndag, marginals, copulas)
print("cbn=", cbn)
print("cbn pdf=", cbn.computePDF([0.5] * d))
print("cbn realization=", cbn.getRealization())
size = 300
sampleLearn = cbn.getSample(size)
sample = cbn.getSample(size)
sampleLearn.exportToCSVFile("samplelearn.csv", ",")
sample.exportToCSVFile("sample.csv", ",")
print("cbn sample=", sample)
logL = 0.0
pdfSample = cbn.computePDF(sample)
pdfSample.exportToCSVFile("pdfSample.csv", ",")
for i in range(size):
m_list = [ot.Uniform(0.0, 1.0)
for i in range(structure.getSize())] # Local marginals
lcc_list = [] # Local Conditional Copulas
for i in range(structure.getSize()):
dim_lcc = structure.getParents(i).getSize() + 1
R = ot.CorrelationMatrix(dim_lcc)
for j in range(dim_lcc):
for k in range(j):
R[j, k] = 0.6
lcc_list.append(ot.Normal([0.0] * dim_lcc, [1.0] * dim_lcc, R).getCopula())
# %%
# Now that we have a NamedDAG structure and a collection of local conditional copulas, we can construct a CBN.
# %%
cbn = otagrum.ContinuousBayesianNetwork(structure, m_list, lcc_list)
# %%
# Having a CBN, we can now sample from it.
# %%
ot.RandomGenerator.SetSeed(10) # Set random seed
sample = cbn.getSample(1000)
train = sample[:-100]
test = sample[-100:]
# %%
# Learning the structure with continuous PC:
# Now that we have data, we can use it to learn the structure with the continuous PC algorithm.
# %%
TTest = otagr.ContinuousTTest(train, alpha)
jointDistributions = []
for i in range(order.getSize()):
dim = 1 + ndag.getParents(i).getSize()
if dim == 1:
bernsteinCopula = ot.Uniform(0.0, 1.0)
else:
K = TTest.GetK(len(train), dim)
indices = [int(n) for n in ndag.getParents(i)]
indices = [i] + indices
bernsteinCopula = ot.EmpiricalBernsteinCopula(
train.getMarginal(indices), K, False)
jointDistributions.append(bernsteinCopula)
#print("jD", jointDistributions)
cbn = otagr.ContinuousBayesianNetwork(ndag, jointDistributions)
ll = 0
for t in test:
#print("contribution", cbn.computeLogPDF(d))
ll += cbn.computeLogPDF(t)
ll /= len(test)
list_loglikelihoods.append(ll)
Loglikelihoods.append(list_loglikelihoods)
# Transposing result matrix
Loglikelihoods = np.reshape(Loglikelihoods, (n_restart, n_samples)).transpose()
Loglikelihoods = np.array(Loglikelihoods, dtype=float)
ll_mean = np.mean(Loglikelihoods, axis=1).reshape((len(Loglikelihoods), 1))
ll_std = np.std(Loglikelihoods, axis=1).reshape((len(Loglikelihoods), 1))