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],
np.nan*np.ones(2))
pass
def test_constant(self):
"""
Test constant categorical nodes
"""
# Basic test
Y = Mixture(2, Gamma, [1, 2, 3], [1, 1, 1])
u = Y._message_to_child()
self.assertAllClose(u[0],
3/1)
# Test with one plate axis
alpha = [[1, 2, 3],
[4, 5, 6]]
Y = Mixture([2, 1], Gamma, alpha, 1)
u = Y._message_to_child()
self.assertAllClose(u[0],
[3, 5])
# Test with two plate axes
alpha = [ [[1, 2, 3],
[4, 5, 6]],
[[7, 8, 9],
[10, 11, 12]] ]
Y = Mixture([[2, 1], [0, 2]], Gamma, alpha, 1)
u = Y._message_to_child()
self.assertAllClose(u[0],
[[3, 5],
[7, 12]])
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], np.nan * np.ones(2))
pass
def test_constant(self):
"""
Test constant categorical nodes
"""
# Basic test
Y = Mixture(2, Gamma, [1, 2, 3], [1, 1, 1])
u = Y._message_to_child()
self.assertAllClose(u[0],
3/1)
# Test with one plate axis
alpha = [[1, 2, 3],
[4, 5, 6]]
Y = Mixture([2, 1], Gamma, alpha, 1)
u = Y._message_to_child()
self.assertAllClose(u[0],
[3, 5])
# Test with two plate axes
alpha = [ [[1, 2, 3],
[4, 5, 6]],
[[7, 8, 9],
[10, 11, 12]] ]
Y = Mixture([[2, 1], [0, 2]], Gamma, alpha, 1)
u = Y._message_to_child()
self.assertAllClose(u[0],
[[3, 5],
[7, 12]])
pass
def test_mixture_with_count_array(self):
"""
Test binomial mixture with varying number of trials
"""
p0 = 0.6
p1 = 0.9
p2 = 0.3
counts = [[10], [5], [3]]
X = Mixture(2, Binomial, counts, [p0, p1, p2])
u = X._message_to_child()
self.assertAllClose(u[0], np.array(counts)[:, 0] * np.array(p2))
# Multi-mixture and count array
# Shape(p) = (2, 1, 3) + ()
p = [
[[0.6, 0.9, 0.8]],
[[0.1, 0.2, 0.3]],
]
# Shape(Z1) = (1, 3) + (2,) -> () + (2,)
Z1 = 1
# Shape(Z2) = (1,) + (3,) -> () + (3,)
Z2 = 2
# Shape(counts) = (5, 1)
counts = [[10], [5], [3], [2], [4]]
# Shape(X) = (5,) + ()
X = Mixture(
Z1,
Mixture,
Z2,
Binomial,
counts,
p,
# NOTE: We mix over axes -3 and -1. But as we first mix over the
# default (-1), then the next mixing happens over -2 (because one
# axis was already dropped).
cluster_plate=-2,
)
self.assertAllClose(X._message_to_child()[0],
np.array(counts)[:, 0] * np.array(p)[Z1, :, Z2])
# Can't have non-singleton axis in counts over the mixed axis
p0 = 0.6
p1 = 0.9
p2 = 0.3
counts = [10, 5, 3]
self.assertRaises(
ValueError,
Mixture,
2,
Binomial,
counts,
[p0, p1, p2],
)
return
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_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_mixture(self):
"""
Test mixture of Bernoulli
"""
P = Mixture([2, 0, 0], Bernoulli, [0.1, 0.2, 0.3])
u = P._message_to_child()
self.assertEqual(len(u), 1)
self.assertAllClose(u[0], [0.3, 0.1, 0.1])
pass
def test_mixture(self):
"""
Test mixture of Bernoulli
"""
P = Mixture([2,0,0], Bernoulli, [0.1, 0.2, 0.3])
u = P._message_to_child()
self.assertEqual(len(u), 1)
self.assertAllClose(u[0], [0.3, 0.1, 0.1])
pass
def test_mixture(self):
"""
Test binomial mixture
"""
X = Mixture(2, Binomial, 10, [0.1, 0.2, 0.3, 0.4])
u = X._message_to_child()
self.assertAllClose(u[0], 3.0)
pass
def test_mixture(self):
"""
Test binomial mixture
"""
X = Mixture(2, Binomial, 10, [0.1, 0.2, 0.3, 0.4])
u = X._message_to_child()
self.assertAllClose(u[0], 3.0)
pass
def test_mixture(self):
"""
Test multinomial mixture
"""
p0 = [0.1, 0.5, 0.2, 0.2]
p1 = [0.5, 0.1, 0.1, 0.3]
p2 = [0.3, 0.2, 0.1, 0.4]
X = Mixture(2, Multinomial, 10, [p0, p1, p2])
u = X._message_to_child()
self.assertAllClose(u[0], 10 * np.array(p2))
pass
def test_mixture(self):
"""
Test multinomial mixture
"""
p0 = [0.1, 0.5, 0.2, 0.2]
p1 = [0.5, 0.1, 0.1, 0.3]
p2 = [0.3, 0.2, 0.1, 0.4]
X = Mixture(2, Multinomial, 10, [p0, p1, p2])
u = X._message_to_child()
self.assertAllClose(u[0],
10*np.array(p2))
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()
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 = X._message_to_parent(0)
self.assertAllClose(m[0],
random.gaussian_logpdf(xx*alpha,
x*alpha*mu,
mumu*alpha,
logalpha,
0))
m = X._message_to_parent(1)
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 = X._message_to_parent(0)
self.assertAllClose(m[0],
random.gaussian_logpdf(xx*alpha,
x*alpha*mu,
mumu*alpha,
logalpha,
0))
m = X._message_to_parent(1)
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 = X._message_to_parent(0)
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 = X._message_to_parent(1)
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)))
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_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()
pass
