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################################################################################
# Copyright (C) 2014 Jaakko Luttinen
#
# This file is licensed under the MIT License.
################################################################################
"""
Unit tests for mixture module.
"""
import warnings
import numpy as np
from bayespy.nodes import (GaussianARD,
Gamma,
Mixture,
Categorical,
Bernoulli,
Multinomial,
Beta,
Gate,
Dirichlet)
from bayespy.utils import random
from bayespy.utils import linalg
from bayespy.utils.misc import TestCase
class TestMixture(TestCase):
def test_init(self):
"""
Test the creation of Mixture node
"""
# Do not accept non-negative cluster plates
z = Categorical(np.random.dirichlet([1,1]))
self.assertRaises(ValueError,
Mixture,
z,
GaussianARD,
GaussianARD(0, 1, plates=(2,)),
Gamma(1, 1, plates=(2,)),
cluster_plate=0)
# Try constructing a mixture without any of the parents having the
# cluster plate axis
z = Categorical(np.random.dirichlet([1,1]))
self.assertRaises(ValueError,
Mixture,
z,
GaussianARD,
GaussianARD(0, 1, plates=()),
Gamma(1, 1, plates=()))
def test_message_to_child(self):
"""
Test the message to child of Mixture node.
"""
K = 3
#
# Estimate moments from parents only
#
# Simple case
mu = GaussianARD([0,2,4], 1,
ndim=0,
plates=(K,))
alpha = Gamma(1, 1,
plates=(K,))
z = Categorical(np.ones(K)/K)
X = Mixture(z, GaussianARD, mu, alpha)
self.assertEqual(X.plates, ())
self.assertEqual(X.dims, ( (), () ))
u = X._message_to_child()
self.assertAllClose(u[0],
2)
self.assertAllClose(u[1],
2**2+1)
# Broadcasting the moments on the cluster axis
mu = GaussianARD(2, 1,
ndim=0,
plates=(K,))
alpha = Gamma(1, 1,
plates=(K,))
z = Categorical(np.ones(K)/K)
X = Mixture(z, GaussianARD, mu, alpha)
self.assertEqual(X.plates, ())
self.assertEqual(X.dims, ( (), () ))
u = X._message_to_child()
self.assertAllClose(u[0],
2)
self.assertAllClose(u[1],
2**2+1)
#
# Estimate moments with observed children
#
pass
def test_message_to_parent(self):
"""
Test the message to parents of Mixture node.
"""
K = 3
# Broadcasting the moments on the cluster axis
Mu = GaussianARD(2, 1,
ndim=0,
plates=(K,))
(mu, mumu) = Mu._message_to_child()
Alpha = Gamma(3, 1,
plates=(K,))
(alpha, logalpha) = Alpha._message_to_child()
z = Categorical(np.ones(K)/K)
X = Mixture(z, GaussianARD, Mu, Alpha)
tau = 4
Y = GaussianARD(X, tau)
y = 5
Y.observe(y)
(x, xx) = X._message_to_child()
m = z._message_from_children()
self.assertAllClose(m[0] * np.ones(K),
random.gaussian_logpdf(xx*alpha,
x*alpha*mu,
mumu*alpha,
logalpha,
0)
* np.ones(K))
m = Mu._message_from_children()
self.assertAllClose(m[0],
1/K * (alpha*x) * np.ones(3))
self.assertAllClose(m[1],
-0.5 * 1/K * alpha * np.ones(3))
# Some parameters do not have cluster plate axis
Mu = GaussianARD(2, 1,
ndim=0,
plates=(K,))
(mu, mumu) = Mu._message_to_child()
Alpha = Gamma(3, 1) # Note: no cluster plate axis!
(alpha, logalpha) = Alpha._message_to_child()
z = Categorical(np.ones(K)/K)
X = Mixture(z, GaussianARD, Mu, Alpha)
tau = 4
Y = GaussianARD(X, tau)
y = 5
Y.observe(y)
(x, xx) = X._message_to_child()
m = z._message_from_children()
self.assertAllClose(m[0] * np.ones(K),
random.gaussian_logpdf(xx*alpha,
x*alpha*mu,
mumu*alpha,
logalpha,
0)
* np.ones(K))
m = Mu._message_from_children()
self.assertAllClose(m[0],
1/K * (alpha*x) * np.ones(3))
self.assertAllClose(m[1],
-0.5 * 1/K * alpha * np.ones(3))
# Cluster assignments do not have as many plate axes as parameters.
M = 2
Mu = GaussianARD(2, 1,
ndim=0,
plates=(K,M))
(mu, mumu) = Mu._message_to_child()
Alpha = Gamma(3, 1,
plates=(K,M))
(alpha, logalpha) = Alpha._message_to_child()
z = Categorical(np.ones(K)/K)
X = Mixture(z, GaussianARD, Mu, Alpha, cluster_plate=-2)
tau = 4
Y = GaussianARD(X, tau)
y = 5 * np.ones(M)
Y.observe(y)
(x, xx) = X._message_to_child()
m = z._message_from_children()
self.assertAllClose(m[0]*np.ones(K),
np.sum(random.gaussian_logpdf(xx*alpha,
x*alpha*mu,
mumu*alpha,
logalpha,
0) *
np.ones((K,M)),
axis=-1))
m = Mu._message_from_children()
self.assertAllClose(m[0] * np.ones((K,M)),
1/K * (alpha*x) * np.ones((K,M)))
self.assertAllClose(m[1] * np.ones((K,M)),
-0.5 * 1/K * alpha * np.ones((K,M)))
# Mixed distribution broadcasts g
# This tests for a found bug. The bug caused an error.
Z = Categorical([0.3, 0.5, 0.2])
X = Mixture(Z, Categorical, [[0.2,0.8], [0.1,0.9], [0.3,0.7]])
m = Z._message_from_children()
#
# Test nested mixtures
#
t1 = [1, 1, 0, 3, 3]
t2 = [2]
p = Dirichlet([1, 1], plates=(4, 3))
X = Mixture(t1, Mixture, t2, Categorical, p)
X.observe([1, 1, 0, 0, 0])
p.update()
self.assertAllClose(
p.phi[0],
[
[[1, 1], [1, 1], [2, 1]],
[[1, 1], [1, 1], [1, 3]],
[[1, 1], [1, 1], [1, 1]],
[[1, 1], [1, 1], [3, 1]],
]
)
# Test sample plates in nested mixtures
t1 = Categorical([0.3, 0.7], plates=(5,))
t2 = [[1], [1], [0], [3], [3]]
t3 = 2
p = Dirichlet([1, 1], plates=(2, 4, 3))
X = Mixture(t1, Mixture, t2, Mixture, t3, Categorical, p)
X.observe([1, 1, 0, 0, 0])
p.update()
self.assertAllClose(
p.phi[0],
[
[
[[1, 1], [1, 1], [1.3, 1]],
[[1, 1], [1, 1], [1, 1.6]],
[[1, 1], [1, 1], [1, 1]],
[[1, 1], [1, 1], [1.6, 1]],
],
[
[[1, 1], [1, 1], [1.7, 1]],
[[1, 1], [1, 1], [1, 2.4]],
[[1, 1], [1, 1], [1, 1]],
[[1, 1], [1, 1], [2.4, 1]],
]
]
)
# Check that Gate and nested Mixture are equal
t1 = Categorical([0.3, 0.7], plates=(5,))
t2 = Categorical([0.1, 0.3, 0.6], plates=(5, 1))
p = Dirichlet([1, 2, 3, 4], plates=(2, 3))
X = Mixture(t1, Mixture, t2, Categorical, p)
X.observe([3, 3, 1, 2, 2])
t1_msg = t1._message_from_children()
t2_msg = t2._message_from_children()
p_msg = p._message_from_children()
t1 = Categorical([0.3, 0.7], plates=(5,))
t2 = Categorical([0.1, 0.3, 0.6], plates=(5, 1))
p = Dirichlet([1, 2, 3, 4], plates=(2, 3))
X = Categorical(Gate(t1, Gate(t2, p)))
X.observe([3, 3, 1, 2, 2])
t1_msg2 = t1._message_from_children()
t2_msg2 = t2._message_from_children()
p_msg2 = p._message_from_children()
self.assertAllClose(t1_msg[0], t1_msg2[0])
self.assertAllClose(t2_msg[0], t2_msg2[0])
self.assertAllClose(p_msg[0], p_msg2[0])
pass
def test_lowerbound(self):
"""
Test log likelihood lower bound for Mixture node
"""
# Mixed distribution broadcasts g
# This tests for a found bug. The bug caused an error.
Z = Categorical([0.3, 0.5, 0.2])
X = Mixture(Z, Categorical, [[0.2,0.8], [0.1,0.9], [0.3,0.7]])
X.lower_bound_contribution()
pass
def test_mask_to_parent(self):
"""
Test the mask handling in Mixture node
"""
K = 3
Z = Categorical(np.ones(K)/K,
plates=(4,5,1))
Mu = GaussianARD(0, 1,
shape=(2,),
plates=(4,K,5))
Alpha = Gamma(1, 1,
plates=(4,K,5,2))
X = Mixture(Z, GaussianARD, Mu, Alpha, cluster_plate=-3)
Y = GaussianARD(X, 1, ndim=1)
mask = np.reshape((np.mod(np.arange(4*5), 2) == 0),
(4,5))
Y.observe(np.ones((4,5,2)),
mask=mask)
self.assertArrayEqual(Z.mask,
mask[:,:,None])
self.assertArrayEqual(Mu.mask,
mask[:,None,:])
self.assertArrayEqual(Alpha.mask,
mask[:,None,:,None])
pass
def test_nans(self):
"""
Test multinomial mixture
"""
# The probabilities p1 cause problems
p0 = [0.1, 0.9]
p1 = [1.0-1e-50, 1e-50]
Z = Categorical([1-1e-10, 1e-10])
X = Mixture(Z, Multinomial, 10, [p0, p1])
u = X._message_to_child()
self.assertAllClose(u[0],
[1, 9])
p0 = [0.1, 0.9]
p1 = [1.0-1e-10, 1e-10]
Z = Categorical([1-1e-50, 1e-50])
X = Mixture(Z, Multinomial, 10, [p0, p1])
u = X._message_to_child()
self.assertAllClose(u[0],
[1, 9])
with warnings.catch_warnings():
warnings.simplefilter("ignore", RuntimeWarning)
warnings.simplefilter("ignore", UserWarning)
p0 = [0.1, 0.9]
p1 = [1.0, 0.0]
X = Mixture(0, Multinomial, 10, [p0, p1])
u = X._message_to_child()
self.assertAllClose(u[0], [1, 9])
pass
def test_random(self):
"""
Test random sampling of mixture node
"""
o = 1e-20
X = Mixture([1, 0, 2], Categorical, [ [o, o, o, 1],
[o, o, 1, o],
[1, o, o, o] ])
x = X.random()
self.assertAllClose(x, [2, 3, 0])
pass
def test_deterministic_mappings(self):
x = Categorical([0.8, 0.2])
y = Mixture(
x,
Categorical,
[
[0.10, 0.90],
[0.00, 1.00],
]
)
y.observe(0)
x.update()
self.assertAllClose(x.u[0], [1, 0])
y.observe(1)
x.update()
p = np.array([0.8*0.9, 0.2*1.0])
self.assertAllClose(x.u[0], p / np.sum(p))
pass
|
