def KSG_learning(data):
print("Build KSG coefficients distribution")
size = data.getSize()
dimension = data.getDimension()
t0 = time()
marginals = [
ot.HistogramFactory().build(data.getMarginal(i))
for i in range(dimension)
]
plot_marginals("KSG_marginals", marginals)
copula = ot.NormalCopulaFactory().build(data)
distribution = ot.ComposedDistribution(marginals, copula)
print("t=", time() - t0, "s")
return distribution
def BuildDistribution(X):
#return ot.FunctionalChaosAlgorithm.BuildDistribution(X)
input_dimension = X.shape[1]
marginals = []
for j in range(input_dimension):
marginals.append(ot.HistogramFactory().build(X[:,j].reshape(-1, 1)))
isIndependent = True
for j in range(input_dimension):
marginalJ = X[:,j].reshape(-1, 1)
for i in range(j + 1, input_dimension):
marginalI = X[:,i].reshape(-1, 1)
testResult = ot.HypothesisTest.Spearman(marginalI, marginalJ)
isIndependent = isIndependent and testResult.getBinaryQualityMeasure()
copula = ot.IndependentCopula(input_dimension)
if not isIndependent:
copula = ot.NormalCopulaFactory().build(X)
distribution = ot.ComposedDistribution(marginals, copula)
return distribution
ax.set_zlabel('$\\varphi_i(\mathbf{x})$')
pl.savefig('2D_identification_eigensolution_%d.png' % i)
pl.close()
# Calculation of the KL coefficients by functional projection using
# Gauss-Legendre quadrature
xi = estimated_random_field.compute_coefficients(sample_paths)
# Statistical inference of the KL coefficients' distribution
kernel_smoothing = ot.KernelSmoothing(ot.Normal())
xi_marginal_distributions = ot.DistributionCollection([
kernel_smoothing.build(xi[:, i][:, np.newaxis])
for i in xrange(truncation_order)
])
try:
xi_copula = ot.NormalCopulaFactory().build(xi)
except RuntimeError:
print('ERR: The normal copula correlation matrix built from the given\n' +
'Spearman correlation matrix is not definite positive.\n' +
'This would require expert judgement on the correlation\n' +
'coefficients significance (using e.g. Spearman test).\n' +
'Assuming an independent copula in the sequel...')
xi_copula = ot.IndependentCopula(truncation_order)
xi_estimated_distribution = ot.ComposedDistribution(xi_marginal_distributions,
xi_copula)
# Matrix plot of the empirical KL coefficients & their estimated distribution
matrix_plot(xi,
ot_distribution=xi_estimated_distribution,
labels=[('$\\xi_{%d}$' % i) for i in xrange(truncation_order)])
pl.suptitle('Karhunen-Loeve coefficients ' +
def NC_marginalKS(data, marginals):
# Third model: marginal KS + normal copula
print("Normal copula")
model = ot.ComposedDistribution(marginals,
ot.NormalCopulaFactory().build(data))
return model
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):
logL += m.log(pdfSample(i, 0))
logL /= size
print("log-l=", logL)
copula = ot.NormalCopulaFactory().buildAsNormalCopula(sampleLearn)
print("copula=", copula)
print("log-l=", copula.computeLogPDF(sample).computeMean()[0])
gr = ot.Graph()
pairs = ot.Pairs(sample)
pairs.setPointStyle("dot")
gr.add(pairs)
import openturns.viewer as otv
view = otv.View(gr, (800, 820), square_axes=True)
view.save("pairs.png")
view.close()
gr = ot.Graph()
pairs = ot.Pairs(copula.getSample(size))
pairs.setPointStyle("dot")
gr.add(pairs)
view = otv.View(gr, (800, 820), square_axes=True)
# In this example we are going to estimate the parameters of a gaussian copula from a sample. # %% from __future__ import print_function 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(500) # %% # Estimate a normal copula distribution = ot.NormalCopulaFactory().build(sample) print(distribution) # %% # The estimated parameters distribution.getParameter() # %% # Draw fitted distribution graph = distribution.drawPDF() view = viewer.View(graph) plt.show()
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
else:
print("pb point=", point, "log pdf=", point_ll)
ll /= s
n_arc = cmiic_dag.getDAG().sizeArcs()
sobol.setReplicationSize(3)
sobol.setBlockSize(1)
sobol.setSeed(2)
sobol.setInterestVariables(['y0', 'y1'])
myStudy.add(sobol)
# 4-b SRC ##
src = persalys.SRCAnalysis('SRC', model1)
src.setSimulationsNumber(20)
src.setSeed(2)
src.setInterestVariables(['y0', 'y1'])
myStudy.add(src)
# 7- data analysis ##
dataAnalysis = persalys.DataAnalysis('DataAnalysis', model3)
myStudy.add(dataAnalysis)
# 8- Marginals inference ##
inference = persalys.InferenceAnalysis('inference', model3)
inference.setInterestVariables(['x_0', 'x_3'])
factories = [ot.NormalFactory(), ot.GumbelFactory()]
inference.setDistributionsFactories('x_3', factories)
inference.setLevel(0.1)
myStudy.add(inference)
# 9- Copula inference ##
copulaInference = persalys.CopulaInferenceAnalysis('copulaInference', model3)
factories = [ot.NormalCopulaFactory(), ot.GumbelCopulaFactory()]
copulaInference.setDistributionsFactories(['x_0', 'x_3'], factories)
myStudy.add(copulaInference)
import openturns as ot
from matplotlib import pyplot as plt
from openturns.viewer import View
ot.RandomGenerator.SetSeed(0)
factory = ot.NormalCopulaFactory()
ref = factory.build()
dimension = ref.getDimension()
if dimension <= 2:
sample = ref.getSample(50)
distribution = factory.build(sample)
if dimension == 1:
distribution.setDescription(['$t$'])
pdf_graph = distribution.drawPDF(256)
cloud = ot.Cloud(sample, ot.Sample(sample.getSize(), 1))
cloud.setColor('blue')
cloud.setPointStyle('fcircle')
pdf_graph.add(cloud)
fig = plt.figure(figsize=(10, 4))
plt.suptitle(str(distribution))
pdf_axis = fig.add_subplot(111)
View(pdf_graph, figure=fig, axes=[pdf_axis], add_legend=False)
else:
sample = ref.getSample(500)
distribution.setDescription(['$t_0$', '$t_1$'])
pdf_graph = distribution.drawPDF([256]*2)
cloud = ot.Cloud(sample)
cloud.setColor('red')
cloud.setPointStyle('fcircle')
pdf_graph.add(cloud)
fig = plt.figure(figsize=(10, 4))
plt.suptitle(str(distribution))
