def BC_marginalKS(data, marginals):
# Fourth model: marginal KS + Bernstein copula
print("Bernstein copula")
# ot.Log.Show(ot.Log.INFO)
model = ot.ComposedDistribution(marginals,
ot.BernsteinCopulaFactory().build(data))
return model
def CBN_PC(data, result_structure_path):
print("CBN with PC")
skeleton_path = result_structure_path.joinpath("skeleton")
skeleton_path.mkdir(parents=True, exist_ok=True)
pdag_path = result_structure_path.joinpath("pdag")
pdag_path.mkdir(parents=True, exist_ok=True)
dag_path = result_structure_path.joinpath("dag")
dag_path.mkdir(parents=True, exist_ok=True)
skeleton_file_name = "skeleton_" + str(size).zfill(7) + ".dot"
skeleton_done = skeleton_path.joinpath(skeleton_file_name).exists()
pdag_file_name = "pdag_" + str(size).zfill(7) + ".dot"
pdag_done = pdag_path.joinpath(pdag_file_name).exists()
dag_file_name = "dag_" + str(size).zfill(7) + ".dot"
dag_done = dag_path.joinpath(dag_file_name).exists()
alpha = 0.01
conditioningSet = 4
learner = otagr.ContinuousPC(data, conditioningSet, alpha)
learner.setVerbosity(True)
if not skeleton_done:
skel = learner.learnSkeleton()
gu.write_graph(
skel,
skeleton_path.joinpath("skeleton_" + str(size).zfill(7) + ".dot"))
if not pdag_done:
pdag = learner.learnPDAG()
gu.write_graph(
pdag, pdag_path.joinpath("pdag_" + str(size).zfill(7) + ".dot"))
if not dag_done:
dag = learner.learnDAG()
gu.write_graph(dag,
dag_path.joinpath("dag_" + str(size).zfill(7) + ".dot"))
else:
dag, names = gu.read_graph(
dag_path.joinpath("dag_" + str(size).zfill(7) + ".dot"))
dag = otagr.NamedDAG(dag, names)
print("Learning parameters")
factories = [
ot.KernelSmoothing(ot.Epanechnikov()),
ot.BernsteinCopulaFactory()
]
ot.Log.SetFile("log")
ot.Log.Show(ot.Log.INFO)
model = otagr.ContinuousBayesianNetworkFactory(factories, dag, alpha,
conditioningSet,
False).build(data)
ot.Log.Show(ot.Log.INFO)
return model
def ot_bernstein_copula_fit(Pared):
sample_Pared = ot.Sample(Pared)
marginals = ot_kernel_Marginals(sample_Pared)
ranksTransf = ot.MarginalTransformationEvaluation(
marginals, ot.MarginalTransformationEvaluation.FROM)
rankSample = ranksTransf(sample_Pared)
bernstein_copula_distribution = ot.BernsteinCopulaFactory().build(
rankSample)
bivariate_distribution = ot.ComposedDistribution(
marginals, bernstein_copula_distribution)
return bivariate_distribution
def CBN_parameter_learning(data, dag):
size = data.getSize()
dimension = data.getDimension()
print(" Learning parameters")
t1 = time()
print(" Learning the CBN parameters")
t2 = time()
ot.ResourceMap.SetAsUnsignedInteger("BernsteinCopulaFactory-kFraction", 2)
ot.ResourceMap.SetAsUnsignedInteger("BernsteinCopulaFactory-MinM",
size // 2 - 2)
ot.ResourceMap.SetAsUnsignedInteger("BernsteinCopulaFactory-MaxM",
size // 2 - 1)
cbn = otagrum.ContinuousBayesianNetworkFactory(ot.HistogramFactory(),
ot.BernsteinCopulaFactory(),
dag, 0, 0,
False).build(data)
print(" t=", time() - t2, "s")
print(" Learning the marginal parameters")
t2 = time()
# marginals = [ot.KernelSmoothing().build(data.getMarginal(i)) for i in range(dimension)]
# marginals = [ot.HistogramFactory().build(data.getMarginal(i)) for i in range(dimension)]
print(" t=", time() - t2, "s")
print(" t=", time() - t1, "s")
return cbn
dimension = est_copula.getDimension()
for d in range(dimension):
print("Is marginal %d a copula ? --> %s" % (d, est_copula.isCopula()))
try:
coll = [ot.GumbelCopula(3.0), ot.ClaytonCopula(3.0), ot.FrankCopula(3.0)]
size = 100
for i, ref_copula in enumerate(coll):
ref_copula = coll[i]
print("Reference copula", str(ref_copula))
sample = ref_copula.getSample(size)
# Default method: log-likelihood
m = ot.BernsteinCopulaFactory.ComputeLogLikelihoodBinNumber(sample)
print("Log-likelihood m=", m)
est_copula = ot.BernsteinCopulaFactory().build(sample, m)
max_error = compute_max_error(ref_copula, est_copula)
print("Max. error=%.5f" % max_error)
check_bernstein_copula(est_copula)
# AMISE method
m = ot.BernsteinCopulaFactory.ComputeAMISEBinNumber(sample)
print("AMISE m=", m)
est_copula = ot.BernsteinCopulaFactory().build(sample, m)
max_error = compute_max_error(ref_copula, est_copula)
print("Max. error=%.5f" % max_error)
check_bernstein_copula(est_copula)
# Penalized Csiszar divergence method
f = ot.SymbolicFunction("t", "-log(t)")
m = ot.BernsteinCopulaFactory.ComputePenalizedCsiszarDivergenceBinNumber(
sample, f)
print("Penalized Csiszar divergence m=", m)
data_ref = data_ref.getMarginal([0, 1, 2, 8])
size = data_ref.getSize() # Size of data
dim = data_ref.getDimension() # Dimension of data
size_draw = min(size, size_draw)
data_draw = data_ref[
0:size_draw] # Number of realizations taken in order to plot figures
print("Processing reference data")
f = figure_path.joinpath("test_pairs_ref.pdf")
pairs(data_draw, f)
print("Bernstein copula")
marginals = get_KS_marginals(data_ref)
KSBC = ot.ComposedDistribution(marginals,
ot.BernsteinCopulaFactory().build(data_ref))
f = figure_path.joinpath("test_pairs_KSBC.pdf")
pairs(KSBC.getSample(size_draw), f)
print("Constructing CBN model")
print("\tLearning structure")
learner = otagr.ContinuousMIIC(data_ref) # Using CPC algorithm
learner.setAlpha(-10)
dag = learner.learnDAG() # Learning DAG
write_graph(dag, result_path.joinpath("test_dag.dot"))
print("\tLearning parameters")
cbn = otagr.ContinuousBayesianNetworkFactory(
ot.KernelSmoothing(ot.Epanechnikov()), ot.BernsteinCopulaFactory(),
# In this example we are going to estimate a normal copula from a sample using non parametric representations. # %% import openturns as ot import openturns.viewer as viewer from matplotlib import pylab as plt ot.Log.Show(ot.Log.NONE) # %% # Create data R = ot.CorrelationMatrix(2) R[1, 0] = 0.4 copula = ot.NormalCopula(R) sample = copula.getSample(30) # %% # Estimate a normal copula using BernsteinCopulaFactory distribution = ot.BernsteinCopulaFactory().build(sample) # %% # Draw fitted distribution graph = distribution.drawPDF() view = viewer.View(graph) # %% # Estimate a normal copula using KernelSmoothing distribution = ot.KernelSmoothing().build(sample).getCopula() graph = distribution.drawPDF() view = viewer.View(graph) plt.show()
# for (i, (train, test)) in enumerate(splits):
for (i, (train, test)) in enumerate(list(splits)):
print("Learning with fold number {}".format(i))
likelihood_curve = []
bic_curve = []
for alpha in alphas:
ot.Log.Show(ot.Log.NONE)
print("\tLearning with alpha={}".format(alpha))
learner = otagr.ContinuousMIIC(
data_ref.select(train)) # Using CMIIC algorithm
learner.setAlpha(alpha)
cmiic_dag = learner.learnDAG() # Learning DAG
ot.Log.Show(ot.Log.NONE)
if True:
cmiic_cbn = otagr.ContinuousBayesianNetworkFactory(
ot.KernelSmoothing(ot.Normal()), ot.BernsteinCopulaFactory(),
cmiic_dag, 0.05, 4, False).build(data_ref.select(train))
else:
cmiic_cbn = otagr.ContinuousBayesianNetworkFactory(
ot.NormalFactory(), ot.NormalCopulaFactory(), cmiic_dag, 0.05,
4, False).build(data_ref.select(train))
# sampled = cmiic_cbn.getSample(1000)
# sampled = (sampled.rank() +1)/(sampled.getSize()+2)
# pairs(sampled, figure_path.joinpath('pairs_test.pdf')
ll = 0
s = 0
for point in data_ref.select(test):
point_ll = cmiic_cbn.computeLogPDF(point)
if np.abs(point_ll) <= 10e20:
s += 1
ll += point_ll
print("children(", nod, ") : ", ndag.getChildren(nod))
order = ndag.getTopologicalOrder()
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)
size = 300
sample = cbn.getSample(size)
# ContinuousBayesianNetworkFactory
marginalsFactory = ot.UniformFactory()
copulasFactory = ot.BernsteinCopulaFactory()
threshold = 0.1
maxParents = 5
factory = otagrum.ContinuousBayesianNetworkFactory(marginalsFactory,
copulasFactory, ndag,
threshold, maxParents)
cbn = factory.build(sample)
print('cbn=', cbn)