def test2DNormalDist(self):
# prepare data
U = dists.J(
[dists.Normal(1.0, .1, 0, 2),
dists.Normal(0.5, .01, 0, 1)])
trainSamples = U.rvs(300)
testSamples = U.rvs(1000)
# build parameter set
dist = dists.KDEDist(trainSamples, bounds=U.getBounds())
samples = dist.rvs(1000, shuffle=True)
# fig = plt.figure()
# plotDensity2d(U)
# fig.show()
#
# fig = plt.figure()
# plotDensity2d(dist)
# plt.scatter(samples[:, 0], samples[:, 1])
# fig.show()
print("quad = %s" % (dblquad(lambda x, y: dist.pdf([x, y]), 0, 2,
lambda _: 0, lambda _: 1), ))
print("mean = %g ~ %g" % (U.mean(), dist.mean()))
print("var = %g ~ %g" % (U.var(), dist.var()))
print("KL = %g" % U.klDivergence(dist, testSamples, testSamples))
print("CE = %g" % dist.crossEntropy(testSamples))
print("MSE = %g" % dist.l2error(U, testSamples, testSamples))
plt.show()
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 test2DNormalMoments(self):
mean = 0
var = 0.5
U = dists.J([dists.Normal(mean, var, -2, 2),
dists.Normal(mean, var, -2, 2)])
trainSamples = U.rvs(10000)
dist = KDEDist(trainSamples)
# -----------------------------------------------
self.assertTrue(np.abs(U.mean() - dist.mean()) < 1e-2, "KDE mean wrong")
self.assertTrue(np.abs(U.var() - dist.var()) < 1e-2, "KDE variance wrong")
def test1DNormalDist(self):
# prepare data
U = dists.Normal(1.85, .3, 0, 3)
trainSamples = np.array([U.rvs(500)]).T
testSamples = np.array([U.rvs(1000)]).T
# build parameter set
dist = KDEDist(trainSamples,
kernelType=KernelType_GAUSSIAN,
bandwidthOptimizationType=
BandwidthOptimizationType_MAXIMUMLIKELIHOOD,
bounds=U.getBounds())
# fig = plt.figure()
# plotDensity1d(U)
# plotDensity1d(dist)
print("quad = %s" % (quad(lambda x: dist.pdf([x]), 0, 3), ))
print("mean = %g ~ %g" % (U.mean(), dist.mean()))
print("var = %g ~ %g" % (U.var(), dist.var()))
print("KL = %g" % U.klDivergence(dist, testSamples, testSamples))
print("CE = %g" % dist.crossEntropy(testSamples))
print("MSE = %g" % dist.l2error(U, testSamples, testSamples))
plt.show()
def test_1DNormalDist_variance(self):
# prepare data
U = dists.Normal(1, 2, -8, 8)
# U = dists.Normal(0.5, .2, 0, 1)
# define linear transformation
trans = JointTransformation()
a, b = 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)
dist = SGDEdist(grid, alpha, bounds=U.getBounds())
fig = plt.figure()
plotDensity1d(U,
alpha_value=0.1,
mean_label="$\mathbb{E}",
interval_label="$\alpha=0.1$")
fig.show()
fig = plt.figure()
plotDensity1d(dist,
alpha_value=0.1,
mean_label="$\mathbb{E}",
interval_label="$\alpha=0.1$")
fig.show()
print("1d: mean = %g ~ %g" % (U.mean(), dist.mean()))
print("1d: var = %g ~ %g" % (U.var(), dist.var()))
plt.show()
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()
