def testProductCopula(self):
U = dists.J([dists.Uniform(0, 1), dists.Uniform(0, 1)])
self.assertEqual(U.mean(), 0.25)
self.assertEqual(U.var(), 1./9 - 1./16)
U = dists.J([dists.TNormal(0, 2, -5, 5)])
self.assertEqual(U.mean(), 0)
self.assertEqual(U.var(), 4)
U = dists.J([dists.TNormal(1, 2, -4, 6), dists.TNormal(2, 3, -3, 7)])
self.assertEqual(U.mean(), 2)
self.assertEqual(U.var(), 5. * 13. - 1. * 4.)
def testDiscretization(self):
epsilon = 1e-14
U = dists.J([dists.Uniform(-1, 2), dists.Uniform(0, 3)])
_, error = U.discretize(level=1, hasBorder=True)
assert error < epsilon
epsilon = 1e-3
U = dists.J([dists.TNormal(0.5, 0.1, 0, 1)])
sgde, error = U.discretize(level=10)
assert error < epsilon
epsilon = 1e-1
U = dists.J([dists.TNormal(0.5, 0.1, 0, 1), dists.Beta(5, 10)])
_, error = U.discretize(10)
assert error < epsilon
def test1DNormalDist(self):
# prepare data
U = dists.TNormal(0.5, .2, -1, 2)
np.random.seed(1234567)
trainSamples = np.array([U.rvs(1000)]).T
testSamples = np.array([U.rvs(1000)]).T
# build parameter set
dist = SGDEdist.byLearnerSGDEConfig(
trainSamples,
config={
"grid_level": 6,
"grid_type": "modlinear",
"grid_maxDegree": 3,
"refinement_numSteps": 0,
"refinement_numPoints": 10,
"solver_threshold": 1e-10,
"solver_verbose": True,
"regularization_type": "Laplace",
"crossValidation_enable": True,
"crossValidation_kfold": 5,
"crossValidation_silent": False,
"sgde_makePositive": False,
"sgde_makePositive_candidateSearchAlgorithm": "fullGrid",
"sgde_makePositive_interpolationAlgorithm": "setToZero",
"sgde_makePositive_verbose": True,
"sgde_unitIntegrand": False
},
bounds=np.array([U.getBounds()]))
fig = plt.figure()
plotDensity1d(U, label="analytic")
plotDensity1d(dist, label="sgde")
plt.legend()
# plt.title("mean = %g ~ %g (err=%g), var = %g ~ %g (err=%g)" % (np.mean(trainSamples),
# dist.mean(),
# np.abs(np.mean(trainSamples) - dist.mean()) / np.mean(trainSamples),
# np.var(trainSamples),
# dist.var(),
# np.abs(np.var(trainSamples) - dist.var()) / np.var(trainSamples)
# ))
print("1d: mean = %g ~ %g (err=%g)" %
(np.mean(trainSamples), dist.mean(),
(np.abs(np.mean(trainSamples) - dist.mean()) /
np.mean(trainSamples))))
print("1d: var = %g ~ %g (err=%g)" %
(np.var(trainSamples), dist.var(),
(np.abs(np.var(trainSamples) - dist.var()) /
np.var(trainSamples))))
print("KL = %g" % U.klDivergence(dist, testSamples, testSamples))
print("CE = %g" % dist.crossEntropy(testSamples))
print("MSE = %g" % dist.l2error(U, testSamples, testSamples))
plt.show()