def test2DNormalDist(self):
# prepare data
U = dists.J(
[dists.Normal(2.0, .5, -1, 4),
dists.Normal(1.0, .5, -1, 3)])
U = dists.J(
[dists.Normal(0.5, .5, -1, 2),
dists.Normal(0.5, .4, -1, 2)])
np.random.seed(1234567)
trainSamples = U.rvs(300)
testSamples = U.rvs(1000)
# build parameter set
dist = SGDEdist.byLearnerSGDEConfig(
trainSamples,
config={
"grid_level": 5,
"grid_type": "modlinear",
"refinement_numSteps": 0,
"refinement_numPoints": 10,
"regularization_type": "Laplace",
"crossValidation_lambda": 0.000562341,
"crossValidation_enable": False,
"crossValidation_kfold": 5,
"crossValidation_silent": False,
"sgde_makePositive": False,
"sgde_makePositive_candidateSearchAlgorithm": "joined",
"sgde_makePositive_interpolationAlgorithm": "setToZero",
"sgde_makePositive_generateConsistentGrid": False,
"sgde_makePositive_verbose": True,
"sgde_unitIntegrand": True
},
bounds=U.getBounds())
fig = plt.figure()
plotDensity2d(U)
fig.show()
fig = plt.figure()
plotSG2d(dist.grid,
dist.alpha,
addContour=True,
show_negative=True,
show_grid_points=True)
fig.show()
print("2d: mean = %g ~ %g" % (U.mean(), dist.mean()))
print("2d: var = %g ~ %g" % (U.var(), dist.var()))
plt.show()
print("KL = %g" % U.klDivergence(dist, testSamples, testSamples))
print("CE = %g" % dist.crossEntropy(testSamples))
print("MSE = %g" % dist.l2error(U, testSamples, testSamples))
def test_2DNormalDist_variance(self):
# prepare data
U = dists.J(
[dists.Normal(2.0, .5, -1, 4),
dists.Normal(1.0, .5, -1, 3)])
# U = dists.J([dists.Normal(0.5, .5, -1, 2),
# dists.Normal(0.5, .4, -1, 2)])
# define linear transformation
trans = JointTransformation()
for a, b in U.getBounds():
trans.add(LinearTransformation(a, b))
# get a sparse grid approximation
grid = Grid.createPolyGrid(U.getDim(), 10)
grid.getGenerator().regular(5)
gs = grid.getStorage()
# now refine adaptively 5 times
p = DataVector(gs.getDimension())
nodalValues = np.ndarray(gs.getSize())
# set function values in alpha
for i in range(gs.getSize()):
gs.getPoint(i).getStandardCoordinates(p)
nodalValues[i] = U.pdf(trans.unitToProbabilistic(p.array()))
# hierarchize
alpha = hierarchize(grid, nodalValues)
# # make positive
# alpha_vec = DataVector(alpha)
# createOperationMakePositive().makePositive(grid, alpha_vec)
# alpha = alpha_vec.array()
dist = SGDEdist(grid, alpha, bounds=U.getBounds())
fig = plt.figure()
plotDensity2d(U)
fig.show()
fig = plt.figure()
plotSG2d(dist.grid,
dist.alpha,
addContour=True,
show_negative=True,
show_grid_points=True)
fig.show()
print("2d: mean = %g ~ %g" % (U.mean(), dist.mean()))
print("2d: var = %g ~ %g" % (U.var(), dist.var()))
plt.show()
def test2DPPF(self):
# prepare data
C = np.array([[0.1, 0.08], [0.08, 0.1]]) / 10.
U = dists.MultivariateNormal([0.5, 0.5], C, 0, 1)
train_samples = U.rvs(1000)
fig = plt.figure()
plotDensity2d(U)
plt.title('true density')
fig.show()
dist = SGDEdist.byLearnerSGDEConfig(train_samples,
config={
"grid_level": 5,
"grid_type": "linear",
"refinement_numSteps": 0,
"refinement_numPoints": 10,
"regularization_type":
"Laplace",
"crossValidation_lambda":
0.000562341,
"crossValidation_enable":
False,
"crossValidation_kfold": 5,
"crossValidation_silent": True
},
bounds=U.getBounds())
fig = plt.figure()
plotDensity2d(dist)
plt.title('estimated SGDE density')
fig.show()
samples = dists.J([dists.Uniform(0, 1), dists.Uniform(0, 1)]).rvs(1000)
fig = plt.figure()
plt.plot(samples[:, 0], samples[:, 1], "o ")
plt.title('uniformly drawn samples')
plt.xlim(0, 1)
plt.ylim(0, 1)
fig.show()
transformed_samples = dist.ppf(samples)
fig = plt.figure()
plt.plot(transformed_samples[:, 0], transformed_samples[:, 1], "o ")
plt.title('transformed samples')
plt.xlim(0, 1)
plt.ylim(0, 1)
fig.show()
plt.show()
def test2DCDFandPPF(self):
# prepare data
C = np.array([[0.1, 0.08], [0.08, 0.1]]) / 10.
U = dists.MultivariateNormal([0.5, 0.5], C, 0, 1)
train_samples = U.rvs(1000)
fig = plt.figure()
plotDensity2d(U)
plt.title('true density')
fig.show()
dist = KDEDist(train_samples, bounds=U.getBounds())
fig = plt.figure()
plotDensity2d(dist)
plt.title('estimated KDE density')
fig.show()
samples = dists.J([dists.Uniform(0, 1),
dists.Uniform(0, 1)]).rvs(1000)
fig = plt.figure()
plt.plot(samples[:, 0], samples[:, 1], "o ")
plt.title('u space')
plt.xlim(0, 1)
plt.ylim(0, 1)
fig.show()
transformed_samples = dist.ppf(samples)
fig = plt.figure()
plt.plot(transformed_samples[:, 0], transformed_samples[:, 1], "o ")
plt.title('x space (transformed)')
plt.xlim(0, 1)
plt.ylim(0, 1)
fig.show()
samples = dist.cdf(transformed_samples)
fig = plt.figure()
plt.plot(samples[:, 0], samples[:, 1], "o ")
plt.title('u space (transformed)')
plt.xlim(0, 1)
plt.ylim(0, 1)
fig.show()
plt.show()
def tesst2DPPF(self):
# prepare data
numDims = 2
mean = 0.5
C = np.array([[0.1, 0.08], [0.08, 0.1]]) / 10.
stddev = np.sqrt(C[0, 0])
U = dists.MultivariateNormal(np.ones(numDims) * mean, C, 0, 1)
dist = NatafDist.normal_marginals(mean,
stddev,
C,
bounds=U.getBounds())
fig = plt.figure()
plotDensity2d(U)
plt.title('true density')
fig.show()
fig = plt.figure()
plotDensity2d(dist)
plt.title('estimated Nataf density')
fig.show()
samples = dists.J([dists.Uniform(0, 1), dists.Uniform(0, 1)]).rvs(1000)
fig = plt.figure()
plt.plot(samples[:, 0], samples[:, 1], "o ")
plt.title('uniformly drawn samples')
plt.xlim(0, 1)
plt.ylim(0, 1)
fig.show()
transformed_samples = dist.ppf(samples)
fig = plt.figure()
plt.plot(transformed_samples[:, 0], transformed_samples[:, 1], "o ")
plt.title('transformed samples')
plt.xlim(0, 1)
plt.ylim(0, 1)
fig.show()
plt.show()
def test2DMarginalize(self):
# prepare data
C = np.array([[0.2, 0.08], [0.08, 0.2]]) / 10.
U = dists.MultivariateNormal([0.5, 0.5], C, 0, 1)
fig = plt.figure()
plotDensity2d(U)
plt.title('true density')
fig.show()
samples = U.rvs(1000)
kde = KDEDist(samples)
# fig = plt.figure()
# plotDensity2d(kde)
# plt.title('estimated KDE density')
# fig.show()
# marginalize
opMarg = createOperationDensityMarginalizeKDE(kde.dist)
kdeX = kde.marginalizeToDimX(0)
kdeY = kde.marginalizeToDimX(1)
fig = plt.figure()
plotDensity1d(kdeX)
plotDensity1d(kdeY)
plt.title('margToDimX denstities')
fig.show()
kdeX = kde.marginalize(1)
kdeY = kde.marginalize(0)
fig = plt.figure()
plotDensity1d(kdeX)
plotDensity1d(kdeY)
plt.title('doMarginalize denstities')
fig.show()
plt.show()
def test2DPPF(self):
# prepare data
C = np.array([[0.1, 0.08], [0.08, 0.1]]) / 10.
U = dists.MultivariateNormal([0.5, 0.5], C, 0, 1)
fig = plt.figure()
plotDensity2d(U)
plt.title('true density')
fig.show()
dist = KDEDist(U.rvs(1000),
kernelType=KernelType_EPANECHNIKOV,
bounds=U.getBounds())
fig = plt.figure()
plotDensity2d(dist)
plt.title('estimated KDE density')
fig.show()
samples = dists.J([dists.Uniform(0, 1),
dists.Uniform(0, 1)]).rvs(1000)
fig = plt.figure()
plt.plot(samples[:, 0], samples[:, 1], "o ")
plt.title('uniformly drawn samples')
plt.xlim(0, 1)
plt.ylim(0, 1)
fig.show()
transformed_samples = dist.ppf(samples)
fig = plt.figure()
plt.plot(transformed_samples[:, 0], transformed_samples[:, 1], "o ")
plt.title('transformed samples')
plt.xlim(0, 1)
plt.ylim(0, 1)
fig.show()
plt.show()
def test2DCovarianceMatrix(self):
# prepare data
np.random.seed(1234567)
C = np.array([[0.3, 0.09], [0.09, 0.3]]) / 10.
U = dists.MultivariateNormal([0.5, 0.5], C, 0, 1)
samples = U.rvs(2000)
kde = KDEDist(samples)
sgde = SGDEdist.byLearnerSGDEConfig(
samples,
bounds=U.getBounds(),
config={
"grid_level": 5,
"grid_type": "linear",
"grid_maxDegree": 1,
"refinement_numSteps": 0,
"refinement_numPoints": 10,
"solver_threshold": 1e-10,
"solver_verbose": False,
"regularization_type": "Laplace",
"crossValidation_lambda": 3.16228e-06,
"crossValidation_enable": False,
"crossValidation_kfold": 5,
"crossValidation_silent": False,
"sgde_makePositive": True,
"sgde_makePositive_candidateSearchAlgorithm": "joined",
"sgde_makePositive_interpolationAlgorithm": "setToZero",
"sgde_generateConsistentGrid": True,
"sgde_unitIntegrand": True
})
sgde_x1 = sgde.marginalizeToDimX(0)
sgde_x2 = sgde.marginalizeToDimX(1)
plt.figure()
plotDensity1d(sgde_x1, label="x1")
plotDensity1d(sgde_x2, label="x2")
plt.title(
"mean: x1=%g, x2=%g; var: x1=%g, x2=%g" %
(sgde_x1.mean(), sgde_x2.mean(), sgde_x1.var(), sgde_x2.var()))
plt.legend()
jsonStr = sgde.toJson()
jsonObject = json.loads(jsonStr)
sgde = Dist.fromJson(jsonObject)
fig = plt.figure()
plotDensity2d(U, addContour=True)
plt.title("analytic")
fig = plt.figure()
plotDensity2d(kde, addContour=True)
plt.title("kde")
fig = plt.figure()
plotDensity2d(sgde, addContour=True)
plt.title("sgde (I(f) = %g)" % (doQuadrature(sgde.grid, sgde.alpha), ))
# print the results
print("E(x) ~ %g ~ %g" % (kde.mean(), sgde.mean()))
print("V(x) ~ %g ~ %g" % (kde.var(), sgde.var()))
print("-" * 60)
print(kde.cov())
print(sgde.cov())
self.assertTrue(np.linalg.norm(C - kde.cov()) < 1e-2, "KDE cov wrong")
self.assertTrue(
np.linalg.norm(np.corrcoef(samples.T) - kde.corrcoeff()) < 1e-1,
"KDE corrcoef wrong")
plt.show()
def test2DCDFandPPF(self, plot=True):
# prepare data
C = np.array([[0.1, 0.08], [0.08, 0.1]]) / 10.
U = dists.MultivariateNormal([0.5, 0.5], C, 0, 1)
train_samples = U.rvs(1000)
if plot:
fig = plt.figure()
plotDensity2d(U)
plt.title('true density')
fig.show()
dist = SGDEdist.byLearnerSGDEConfig(train_samples,
config={
"grid_level": 5,
"grid_type":
"polyClenshawCurtis",
"refinement_numSteps": 0,
"refinement_numPoints": 10,
"regularization_type":
"Laplace",
"crossValidation_lambda":
0.000562341,
"crossValidation_enable":
False,
"crossValidation_kfold": 5,
"crossValidation_silent": True,
"sgde_makePositive": False
},
bounds=U.getBounds())
if plot:
fig = plt.figure()
plotDensity2d(dist)
plt.title('estimated SGDE density')
fig.show()
samples = dists.J([dists.Uniform(0, 1), dists.Uniform(0, 1)]).rvs(500)
if plot:
fig = plt.figure()
plt.plot(samples[:, 0], samples[:, 1], "o ")
plt.title('u space')
plt.xlim(0, 1)
plt.ylim(0, 1)
fig.show()
else:
print("-" * 80)
print(samples)
transformed_samples = dist.ppf(samples, shuffle=False)
if plot:
fig = plt.figure()
plt.plot(transformed_samples[:, 0], transformed_samples[:, 1],
"o ")
plt.title('x space (transformed)')
plt.xlim(0, 1)
plt.ylim(0, 1)
fig.show()
else:
print("-" * 80)
print(transformed_samples)
samples = dist.cdf(transformed_samples, shuffle=False)
if plot:
fig = plt.figure()
plt.plot(samples[:, 0], samples[:, 1], "o ")
plt.title('u space (transformed)')
plt.xlim(0, 1)
plt.ylim(0, 1)
fig.show()
plt.show()
else:
print("-" * 80)
print(samples)
def test2DNormalMoments(self):
mean = 0
var = 0.5
U = dists.J(
[dists.Normal(mean, var, -2, 2),
dists.Normal(mean, var, -2, 2)])
np.random.seed(1234567)
trainSamples = U.rvs(1000)
dist = SGDEdist.byLearnerSGDEConfig(trainSamples,
config={
"grid_level": 5,
"grid_type": "linear",
"refinement_numSteps": 0,
"refinement_numPoints": 10,
"regularization_type":
"Laplace",
"crossValidation_lambda":
0.000562341,
"crossValidation_enable":
False,
"crossValidation_kfold": 5,
"crossValidation_silent": True,
"sgde_makePositive": True
},
bounds=U.getBounds())
samples_dist = dist.rvs(1000, shuffle=True)
kde = KDEDist(trainSamples)
samples_kde = kde.rvs(1000, shuffle=True)
# -----------------------------------------------
self.assertTrue(
np.abs(U.mean() - dist.mean()) < 1e-2, "SGDE mean wrong")
self.assertTrue(
np.abs(U.var() - dist.var()) < 4e-2, "SGDE variance wrong")
# -----------------------------------------------
# print the results
print("E(x) ~ %g ~ %g" % (kde.mean(), dist.mean()))
print("V(x) ~ %g ~ %g" % (kde.var(), dist.var()))
print(
"log ~ %g ~ %g" %
(kde.crossEntropy(trainSamples), dist.crossEntropy(trainSamples)))
print("-" * 60)
print(dist.cov())
print(kde.cov())
sgde_x1 = dist.marginalizeToDimX(0)
kde_x1 = kde.marginalizeToDimX(0)
plt.figure()
plotDensity1d(U.getDistributions()[0], label="analytic")
plotDensity1d(sgde_x1, label="sgde")
plotDensity1d(kde_x1, label="kde")
plt.title("mean: sgde=%g, kde=%g; var: sgde=%g, kde=%g" %
(sgde_x1.mean(), kde_x1.mean(), sgde_x1.var(), kde_x1.var()))
plt.legend()
fig = plt.figure()
plotDensity2d(U, addContour=True)
plt.title("analytic")
fig = plt.figure()
plotDensity2d(kde, addContour=True)
plt.scatter(samples_kde[:, 0], samples_kde[:, 1])
plt.title("kde")
fig = plt.figure()
plotDensity2d(dist, addContour=True)
plt.scatter(samples_dist[:, 0], samples_dist[:, 1])
plt.title(
"sgde (I(f) = %g)" %
(np.prod(U.getBounds()) * doQuadrature(dist.grid, dist.alpha), ))
plt.show()
