num_comp = 1 # The model model = TestModel0() # The prior log_p_x = MultivariateNormal(mu=[0]) log_p_z_fake = FlatPDF(model.num_output) log_p_x_ext = PDFCollection([log_p_x, log_p_z_fake]) # The isotropic Likelihood log_p_z_given_x = UncertaintyPropagationLikelihood(model, alpha=100.) # The joint log_p = Joint(log_p_z_given_x, log_p_x_ext) # The approximating distribution log_q = MixtureOfMultivariateNormals.create(log_p.num_dim, num_comp) # Build the ELBO # Pick an entropy approximation entropy = FirstOrderEntropyApproximation() # Pick an approximation for the expectation of the joint expectation_functional = ThirdOrderExpectationFunctional(log_p) # Build the ELBO elbo = EvidenceLowerBound(entropy, expectation_functional) print 'ELBO:' print str(elbo) # Optimize the elbo optimizer = Optimizer(elbo) C_bounds = tuple((1e-32, None) for i in xrange(log_q.num_comp * log_q.num_dim))
import numpy as np
import matplotlib.pyplot as plt
import sys
import os
sys.path.insert(0, os.path.abspath('.'))
from vuq import MixtureOfMultivariateNormals
from vuq import MonteCarloEntropyApproximation
from vuq import FirstOrderEntropyApproximation
from vuq import EntropyLowerBound
# Number of components for the test
num_dim = 1
# Create a random multivariate normal
q = MixtureOfMultivariateNormals.create(num_dim, 1) # With one component first
# Create the entropy approximation
S0 = FirstOrderEntropyApproximation()
# Create a monte carlo approximation to the entropy
Smc = MonteCarloEntropyApproximation(num_samples=100)
# The lower bound to the entropy
Sl = EntropyLowerBound()
# The first order approximation to the entropy
print 'S0[q] =', S0(q)['S']
# The lower bound to the entropy
print 'Sl[q] =', Sl.eval(q)
num_comp = 5 # The model model = TestModel1() # The prior log_p_x = MultivariateNormal(mu=[0]) log_p_z_fake = FlatPDF(model.num_output) log_p_x_ext = PDFCollection([log_p_x, log_p_z_fake]) # The isotropic Likelihood log_p_z_given_x = UncertaintyPropagationLikelihood(model, alpha=1e-1) # The joint log_p = Joint(log_p_z_given_x, log_p_x_ext) # The approximating distribution log_q = MixtureOfMultivariateNormals.create(log_p.num_dim, num_comp) # Build the ELBO # Pick an entropy approximation entropy = FirstOrderEntropyApproximation() # Pick an approximation for the expectation of the joint expectation_functional = ThirdOrderExpectationFunctional(log_p) # Build the ELBO elbo = EvidenceLowerBound(entropy, expectation_functional) print 'ELBO:' print str(elbo) # Optimize the elbo optimizer = FullOptimizer(elbo) C_bounds = tuple((1e-32, None) for i in xrange(log_q.num_comp * log_q.num_dim))
if k != j:
C_new[i, k, j] += h
q.C = C_new
Sph = S0.eval(q)[0]
J[i, j, k] = (Sph - S) / h
if k != j:
J[i, j, k] *= 0.5
q.C = C
return J
# Number of components for the test
num_dim = 1
# Create a random multivariate normal
q = MixtureOfMultivariateNormals.create(num_dim, 2) # With one component first
# Create the entropy approximation
#S0 = FirstOrderEntropyApproximation()
S0 = EntropyLowerBound()
# Create a monte carlo approximation to the entropy
Smc = MonteCarloEntropyApproximation(num_samples=100)
# Try it out with more components
print 'Doing it with two components...'
q = MixtureOfMultivariateNormals.create(num_dim, 2)
#q.comp[0].C = np.array([[2]])
#q.w = np.array([0.3, 0.7])
print str(q)
# Evaluate the entropy