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 test1DCDFandPPF(self):
# prepare data
U = Normal(0.5, 0.1, 0, 1)
train_samples = U.rvs(1000).reshape(1000, 1)
dist = KDEDist(train_samples, kernelType=KernelType_EPANECHNIKOV)
rc('font', **{'size': 18})
fig = plt.figure()
x = np.linspace(0, 1, 1000)
plt.plot(x, dist.cdf(x), label="estimated")
plt.plot(x, [U.cdf(xi) for xi in x], label="analytic")
plt.legend(loc="lower right")
fig.show()
fig = plt.figure()
plt.hist(train_samples, normed=True)
plotDensity1d(U, label="analytic")
plotDensity1d(dist, label="estimated")
plt.title("original space")
plt.legend()
fig.show()
transformed_samples = dist.cdf(train_samples)
fig = plt.figure()
plt.hist(transformed_samples, normed=True)
plt.title("uniform space")
fig.show()
transformed_samples = dist.ppf(transformed_samples)
fig = plt.figure()
plt.hist(transformed_samples, normed=True)
plotDensity1d(U, label="analytic")
plotDensity1d(dist, label="estimated")
plt.title("original space")
plt.legend()
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()