# Source code for GPy.testing.rv_transformation_tests

# Written by Ilias Bilionis
"""
Test if hyperparameters in models are properly transformed.
"""

import unittest
import numpy as np
import scipy.stats as st
import GPy

[docs]class TestModel(GPy.core.Model):
"""
A simple GPy model with one parameter.
"""
def __init__(self, theta=1.):
super(TestModel, self).__init__('test_model')
theta = GPy.core.Param('theta', theta)

[docs]    def log_likelihood(self):
return 0.

[docs]class RVTransformationTestCase(unittest.TestCase):

def _test_trans(self, trans):
m = TestModel()
prior = GPy.priors.LogGaussian(.5, 0.1)
m.theta.set_prior(prior)
m.theta.unconstrain()
m.theta.constrain(trans)
# The PDF of the transformed variables
p_phi = lambda phi : np.exp(-m._objective_grads(phi)[0])
# To the empirical PDF of:
theta_s = prior.rvs(1e5)
phi_s = trans.finv(theta_s)
# which is essentially a kernel density estimation
kde = st.gaussian_kde(phi_s)
# We will compare the PDF here:
phi = np.linspace(phi_s.min(), phi_s.max(), 100)
# The transformed PDF of phi should be this:
pdf_phi = np.array([p_phi(p) for p in phi])
# UNCOMMENT TO SEE GRAPHICAL COMPARISON
#import matplotlib.pyplot as plt
#fig, ax = plt.subplots()
#ax.hist(phi_s, normed=True, bins=100, alpha=0.25, label='Histogram')
#ax.plot(phi, kde(phi), '--', linewidth=2, label='Kernel Density Estimation')
#ax.plot(phi, pdf_phi, ':', linewidth=2, label='Transformed PDF')
#ax.set_xlabel(r'transformed $\theta$', fontsize=16)
#ax.set_ylabel('PDF', fontsize=16)
#plt.legend(loc='best')
#plt.show(block=True)
# END OF PLOT
# The following test cannot be very accurate
self.assertTrue(np.linalg.norm(pdf_phi - kde(phi)) / np.linalg.norm(kde(phi)) <= 1e-1)

np.random.seed(1234)
m = TestModel(np.random.uniform(.5, 1.5, 20))
prior = GPy.priors.LogGaussian(.5, 0.1)
m.theta.set_prior(prior)
m.theta.constrain(trans)
m.randomize()
print(m)

[docs]    def test_Logexp(self):
self._test_trans(GPy.constraints.Logexp())

[docs]    @unittest.skip("Gradient not checking right, @jameshensman what is going on here?")

[docs]    def test_Exponent(self):
self._test_trans(GPy.constraints.Exponent())

[docs]    @unittest.skip("Gradient not checking right, @jameshensman what is going on here?")

if __name__ == '__main__':
unittest.main()
quit()
m = TestModel()
prior = GPy.priors.LogGaussian(0., .9)
m.theta.set_prior(prior)

# The following should return the PDF in terms of the transformed quantities
p_phi = lambda phi : np.exp(-m._objective_grads(phi)[0])

# Let's look at the transformation phi = log(exp(theta - 1))
trans = GPy.constraints.Exponent()
m.theta.constrain(trans)
# Plot the transformed probability density
phi = np.linspace(-8, 8, 100)
fig, ax = plt.subplots()
# Let's draw some samples of theta and transform them so that we see
# which one is right
theta_s = prior.rvs(10000)
# Transform it to the new variables
phi_s = trans.finv(theta_s)
# And draw their histogram
ax.hist(phi_s, normed=True, bins=100, alpha=0.25, label='Empirical')
# This is to be compared to the PDF of the model expressed in terms of these new
# variables
ax.plot(phi, [p_phi(p) for p in phi], label='Transformed PDF', linewidth=2)
ax.set_xlim(-3, 10)
ax.set_xlabel(r'transformed $\theta$', fontsize=16)
ax.set_ylabel('PDF', fontsize=16)
plt.legend(loc='best')
# Now let's test the gradients