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 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()