def testExp2d(self):
trainSamples = np.loadtxt("exp_2d.csv").T
# build parameter set
dist = SGDEdist.byLearnerSGDEConfig(
trainSamples,
config={
"grid_level": 7,
"grid_type": "linear",
"grid_maxDegree": 1,
"refinement_numSteps": 0,
"refinement_numPoints": 10,
"solver_threshold": 1e-10,
"solver_verbose": False,
"regularization_type": "Laplace",
"crossValidation_lambda": 0.000562341,
"crossValidation_enable": False,
"crossValidation_kfold": 5,
"crossValidation_silent": False,
"sgde_makePositive": True,
"sgde_makePositive_candidateSearchAlgorithm": "joined",
"sgde_makePositive_interpolationAlgorithm":
"interpolateBoundaries1d",
"sgde_unitIntegrand": True
})
fig, ax, _ = plotDensity3d(dist)
ax.scatter(trainSamples[:, 0], trainSamples[:, 1],
np.zeros(trainSamples.shape[0]))
ax.set_title("vol=%.12f" % dist.vol)
fig.show()
plt.show()
def testExpPoly2d(self):
trainSamples = np.loadtxt("exp_2d.csv").T
# build parameter set
dist_sgde = SGDEdist.byLearnerSGDEConfig(
trainSamples,
config={
"grid_level": 4,
"grid_type": "modpoly",
"grid_maxDegree": 6,
"refinement_numSteps": 0,
"refinement_numPoints": 10,
"solver_threshold": 1e-10,
"solver_verbose": True,
"regularization_type": "Laplace",
"crossValidation_lambda": 0.000562341,
"crossValidation_enable": False,
"crossValidation_kfold": 5,
"crossValidation_silent": True,
"sgde_makePositive": False,
"sgde_makePositive_candidateSearchAlgorithm": "joined",
"sgde_makePositive_interpolationAlgorithm": "setToZero",
"sgde_makePositive_verbose": True,
"sgde_unitIntegrand": True
})
# build parameter set
dist_kde = dists.KDEDist(
trainSamples,
kernelType=KernelType_GAUSSIAN,
bandwidthOptimizationType=BandwidthOptimizationType_SILVERMANSRULE)
# fig = plt.figure()
# plotSG2d(dist.grid, dist.alpha, show_grid_points=True)
# plt.scatter(trainSamples[:, 0], trainSamples[:, 1], np.zeros(trainSamples.shape[0]))
# plt.title("%.12f" % dist.vol)
fig, _, _ = plotDensity3d(dist_sgde)
plt.title("SGDE: vol=%g" % dist_sgde.vol)
fig, _, _ = plotDensity3d(dist_kde)
plt.title("KDE: vol=1.0")
plt.show()
samples = U.rvs(1000)
testSamples = U.rvs(1000)
# ---------- using SGDE from SG++ ------------------------
dist = SGDEdist.byLearnerSGDEConfig(samples,
config={"grid_level": 6,
"grid_type": "Linear",
"refinement_numSteps": 0,
"refinement_numPoints": 3,
"regularization_type": "Laplace",
"crossValidation_lambda": 0.000562341,
"crossValidation_enable": False,
"crossValidation_kfold": 5,
"crossValidation_silent": False},
bounds=U.getBounds())
fig, ax = plotDensity3d(U)
ax.set_title("true density")
fig.show()
fig, ax, _ = plotSG3d(dist.grid, dist.alpha)
ax.set_title("estimated density")
fig.show()
print("mean = %g ~ %g" % (m.prod(), dist.mean()))
print("var = %g ~ %g" % (np.var(testSamples), dist.var()))
print("KL-divergence = %g" % U.klDivergence(dist, testSamples, testSamples))
print("cross entropy = %g" % dist.crossEntropy(testSamples))
print("MSE = %g" % dist.l2error(U, testSamples, testSamples))
# sampling
uniform_samples = np.random.random((1000, 2))
samples = dist.ppf(uniform_samples)
# dist = MultivariateNormal(mu, cov, 0, 1) # problems in 3d/l2
# dist = J([Beta(5, 4, 0, 1)] * numDims) # problems in 5d/l3
# dist = J([Lognormal(0.2, 0.7, 0, 1)] * numDims) # problems in 5d/l3
trainSamples = dist.rvs(1000)
testSamples = dist.rvs(1000)
# plot analytic density
if numDims == 2 and plot:
fig = plt.figure()
plotDensity2d(dist)
plt.title("analytic, kldivergence = %g" %
dist.klDivergence(dist, testSamples))
fig.show()
fig, ax = plotDensity3d(dist)
ax.set_xlabel(r"$x_1$")
ax.set_ylabel(r"$x_2$")
ax.set_zlabel(r"$f(x_1, x_2)$")
fig.show()
# get a sparse grid approximation
grid = Grid.createGrid(gridConfig)
gridGen = grid.getGenerator()
gridGen.regular(level)
gs = grid.getStorage()
# now refine adaptively 5 times
p = DataVector(gs.getDimension())
alpha = DataVector(gs.getSize())