def test_recover_lambert(self):
# Generate data from a normal, then apply the W transform, and check if we can recover parameters
# See Table 2 of Georg's paper
# These results seem a little worse, but we'd have to run many replications to directly compare.
mu, sigma = 0, 1
# print ('del_true\tns\tmu\tsigma\tdelta').expandtabs(10)
for delta in [0, 1./3, 1., 1.5]:
for n in [50, 100, 1000]:
x = np.random.normal(loc=mu, scale=sigma, size=n)
y = g.inverse(x, (mu, sigma, delta))
mu_prime, sigma_prime, delta_prime = g.igmm(y)
print(('%0.3f\t%d\t%0.3f\t%0.3f\t%0.3f' % (delta, n, mu_prime, sigma_prime, delta_prime)).expandtabs(10))
assert np.abs(mu - mu_prime) < 10. / np.sqrt(n)
assert np.abs(sigma - sigma_prime) < 10. / np.sqrt(n)
assert np.abs(delta - delta_prime) < 10. / np.sqrt(n)
def test_recover_lambert():
# Generate data from a normal, then apply the W transform, and check if we can recover parameters
# See Table 2 of Georg's paper
# These results seem a little worse, but we'd have to run many replications to directly compare.
mu, sigma = 0, 1
print ("del_true\tns\tmu\tsigma\tdelta").expandtabs(10)
for delta in [0, 1.0 / 3, 1.0, 1.5]:
for n in [50, 100, 1000]:
x = np.random.normal(loc=mu, scale=sigma, size=n)
y = g.inverse(x, (mu, sigma, delta))
mu_prime, sigma_prime, delta_prime = g.igmm(y)
print ("%0.3f\t%d\t%0.3f\t%0.3f\t%0.3f" % (delta, n, mu_prime, sigma_prime, delta_prime)).expandtabs(10)
assert np.abs(mu - mu_prime) < 10.0 / np.sqrt(n)
assert np.abs(sigma - sigma_prime) < 10.0 / np.sqrt(n)
assert np.abs(delta - delta_prime) < 10.0 / np.sqrt(n)
def test_normality_increase_lambert(self):
# Generate random data and check that it is more normal after inference
for i, y in enumerate([np.random.standard_cauchy(size=ns), experimental_data]):
print('Distribution %d' % i)
print('Before')
print(('anderson: %0.3f\tshapiro: %0.3f' % (anderson(y)[0], shapiro(y)[0])).expandtabs(30))
stats.probplot(y, dist="norm", plot=plt)
plt.savefig(os.path.join(self.test_dir, '%d_before.png' % i))
plt.clf()
tau = g.igmm(y)
x = g.w_t(y, tau)
print('After')
print(('anderson: %0.3f\tshapiro: %0.3f' % (anderson(x)[0], shapiro(x)[0])).expandtabs(30))
stats.probplot(x, dist="norm", plot=plt)
plt.savefig(os.path.join(self.test_dir, '%d_after.png' % i))
plt.clf()
def test_normality_increase_lambert():
# Generate random data and check that it is more normal after inference
for i, y in enumerate([np.random.standard_cauchy(size=ns), experimental_data]):
print "Distribution %d" % i
print "Before"
print ("anderson: %0.3f\tshapiro: %0.3f" % (anderson(y)[0], shapiro(y)[0])).expandtabs(30)
stats.probplot(y, dist="norm", plot=pylab)
pylab.savefig("%d_before.png" % i)
pylab.clf()
tau = g.igmm(y)
x = g.w_t(y, tau)
print "After"
print ("anderson: %0.3f\tshapiro: %0.3f" % (anderson(x)[0], shapiro(x)[0])).expandtabs(30)
stats.probplot(x, dist="norm", plot=pylab)
pylab.savefig("%d_after.png" % i)
pylab.clf()