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################################################################################
# Copyright (C) 2015 Jaakko Luttinen
#
# This file is licensed under the MIT License.
################################################################################
"""
Unit tests for `wishart` module.
"""
import numpy as np
from scipy import special
from .. import gaussian
from bayespy.nodes import (Gaussian,
Wishart)
from ...vmp import VB
from bayespy.utils import misc
from bayespy.utils import linalg
from bayespy.utils import random
from bayespy.utils.misc import TestCase
def _student_logpdf(y, mu, Cov, nu):
D = np.shape(y)[-1]
return (special.gammaln((nu+D)/2)
- special.gammaln(nu/2)
- 0.5 * D * np.log(nu)
- 0.5 * D * np.log(np.pi)
- 0.5 * np.linalg.slogdet(Cov)[1]
- 0.5 * (nu+D) * np.log(1+1/nu*np.einsum('...i,...ij,...j->...',
y-mu,
np.linalg.inv(Cov),
y-mu)))
class TestWishart(TestCase):
def test_lower_bound(self):
"""
Test the Wishart VB lower bound
"""
#
# By having the Wishart node as the only latent node, VB will give exact
# results, thus the VB lower bound is the true marginal log likelihood.
# Thus, check that they are equal. The true marginal likelihood is the
# multivariate Student-t distribution.
#
np.random.seed(42)
D = 3
n = (D-1) + np.random.uniform(0.1, 0.5)
V = random.covariance(D)
Lambda = Wishart(n, V)
mu = np.random.randn(D)
Y = Gaussian(mu, Lambda)
y = np.random.randn(D)
Y.observe(y)
Lambda.update()
L = Y.lower_bound_contribution() + Lambda.lower_bound_contribution()
mu = mu
nu = n + 1 - D
Cov = V / nu
self.assertAllClose(L,
_student_logpdf(y,
mu,
Cov,
nu))
pass
def test_moments(self):
"""
Test the moments of Wishart node
"""
np.random.seed(42)
# Test prior moments
D = 3
n = (D-1) + np.random.uniform(0.1,2)
V = random.covariance(D)
Lambda = Wishart(n, V)
Lambda.update()
u = Lambda.get_moments()
self.assertAllClose(u[0],
n*np.linalg.inv(V),
msg='Mean incorrect')
self.assertAllClose(u[1],
(np.sum(special.digamma((n - np.arange(D))/2))
+ D*np.log(2)
- np.linalg.slogdet(V)[1]),
msg='Log determinant incorrect')
# Test posterior moments
D = 3
n = (D-1) + np.random.uniform(0.1,2)
V = random.covariance(D)
Lambda = Wishart(n, V)
mu = np.random.randn(D)
Y = Gaussian(mu, Lambda)
y = np.random.randn(D)
Y.observe(y)
Lambda.update()
u = Lambda.get_moments()
n = n + 1
V = V + np.outer(y-mu, y-mu)
self.assertAllClose(u[0],
n*np.linalg.inv(V),
msg='Mean incorrect')
self.assertAllClose(u[1],
(np.sum(special.digamma((n - np.arange(D))/2))
+ D*np.log(2)
- np.linalg.slogdet(V)[1]),
msg='Log determinant incorrect')
pass
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