def test_gaussian_mixture_plot():
"""
Test the gaussian_mixture plotting function.
The code is from http://www.bayespy.org/examples/gmm.html
"""
np.random.seed(1)
y0 = np.random.multivariate_normal([0, 0], [[1, 0], [0, 0.02]], size=50)
y1 = np.random.multivariate_normal([0, 0], [[0.02, 0], [0, 1]], size=50)
y2 = np.random.multivariate_normal([2, 2], [[1, -0.9], [-0.9, 1]], size=50)
y3 = np.random.multivariate_normal([-2, -2], [[0.1, 0], [0, 0.1]], size=50)
y = np.vstack([y0, y1, y2, y3])
bpplt.pyplot.plot(y[:, 0], y[:, 1], 'rx')
N = 200
D = 2
K = 10
alpha = Dirichlet(1e-5 * np.ones(K), name='alpha')
Z = Categorical(alpha, plates=(N, ), name='z')
mu = Gaussian(np.zeros(D), 1e-5 * np.identity(D), plates=(K, ), name='mu')
Lambda = Wishart(D, 1e-5 * np.identity(D), plates=(K, ), name='Lambda')
Y = Mixture(Z, Gaussian, mu, Lambda, name='Y')
Z.initialize_from_random()
Q = VB(Y, mu, Lambda, Z, alpha)
Y.observe(y)
Q.update(repeat=1000)
bpplt.gaussian_mixture_2d(Y, scale=2)
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 _run(self, x, K=25, beta=0.5, alpha=0.00001, hinton_plot=False, end=False):
'''Only to be used when doing parameter optimization.'''
self.participant_list = x[0]
N = len(x[0]) #number of data points (i.e. WCS participants)
D = np.shape(x[1])[1] #number of features
#K = 20 #number of initial clusters
R = Dirichlet(K*[alpha],
name='R')
Z = Categorical(R,
plates=(N,1),
name='Z')
P = Beta([beta, beta],
plates=(D,K),
name='P')
X = Mixture(Z, Bernoulli, P)
Q = VB(Z, R, X, P)
P.initialize_from_random()
X.observe(x[1])
Q.update(repeat=1000)
log_likelihood = Q.L[Q.iter-1]
if hinton_plot:
bpplt.hinton(Z)
bpplt.pyplot.show()
bpplt.hinton(R)
bpplt.pyplot.show()
#Get the weight matrix stored in Z (weights determine which cluster data point belongs to)
z = Z._message_to_child()[0]
z = z * np.ones(Z.plates+(1,))
z = np.squeeze(z)
self.z = z
#Get the weights stored in R (proportional to the size of the clusters)
r = np.exp(R._message_to_child()[0])
r = r * np.ones(R.plates+(1,))
r = np.squeeze(r)
self.r = r
#Get the cluster assignment of each data point
self.c_assign = np.argmax(self.z, axis=1)
return log_likelihood
def test_init(self):
"""
Test the creation of categorical nodes.
"""
# Some simple initializations
X = Categorical([0.1, 0.3, 0.6])
X = Categorical(Dirichlet([5,4,3]))
# Check that plates are correct
X = Categorical([0.1, 0.3, 0.6], plates=(3,4))
self.assertEqual(X.plates,
(3,4))
X = Categorical(0.25*np.ones((2,3,4)))
self.assertEqual(X.plates,
(2,3))
X = Categorical(Dirichlet([2,1,9], plates=(3,4)))
self.assertEqual(X.plates,
(3,4))
# Probabilities not a vector
self.assertRaises(ValueError,
Categorical,
0.5)
# Invalid probability
self.assertRaises(ValueError,
Categorical,
[-0.5, 1.5],
n=10)
self.assertRaises(ValueError,
Categorical,
[0.5, 1.5],
n=10)
# Inconsistent plates
self.assertRaises(ValueError,
Categorical,
0.25*np.ones((2,4)),
plates=(3,),
n=10)
# Explicit plates too small
self.assertRaises(ValueError,
Categorical,
0.25*np.ones((2,4)),
plates=(1,),
n=10)
pass
def test_initialization(self):
"""
Test initialization of categorical nodes
"""
# Test initialization from random
with warnings.catch_warnings():
warnings.simplefilter("ignore", RuntimeWarning)
Z = Categorical([[0.0, 1.0, 0.0], [0.0, 0.0, 1.0]])
Z.initialize_from_random()
u = Z._message_to_child()
self.assertAllClose(u[0], [[0, 1, 0], [0, 0, 1]])
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_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_initialization(self):
"""
Test initialization of categorical nodes
"""
# Test initialization from random
with warnings.catch_warnings(record=True) as w:
Z = Categorical([[0.0, 1.0, 0.0],
[0.0, 0.0, 1.0]])
Z.initialize_from_random()
u = Z._message_to_child()
self.assertAllClose(u[0],
[[0, 1, 0],
[0, 0, 1]])
pass
def _setup_bernoulli_mixture():
"""
Setup code for the hinton tests.
This code is from http://www.bayespy.org/examples/bmm.html
"""
np.random.seed(1)
p0 = [0.1, 0.9, 0.1, 0.9, 0.1, 0.9, 0.1, 0.9, 0.1, 0.9]
p1 = [0.1, 0.1, 0.1, 0.1, 0.1, 0.9, 0.9, 0.9, 0.9, 0.9]
p2 = [0.9, 0.9, 0.9, 0.9, 0.9, 0.1, 0.1, 0.1, 0.1, 0.1]
p = np.array([p0, p1, p2])
z = random.categorical([1 / 3, 1 / 3, 1 / 3], size=100)
x = random.bernoulli(p[z])
N = 100
D = 10
K = 10
R = Dirichlet(K * [1e-5], name='R')
Z = Categorical(R, plates=(N, 1), name='Z')
P = Beta([0.5, 0.5], plates=(D, K), name='P')
X = Mixture(Z, Bernoulli, P)
Q = VB(Z, R, X, P)
P.initialize_from_random()
X.observe(x)
Q.update(repeat=1000)
return (R, P, Z)
def test_gaussian_mixture_plot():
"""
Test the gaussian_mixture plotting function.
The code is from http://www.bayespy.org/examples/gmm.html
"""
np.random.seed(1)
y0 = np.random.multivariate_normal([0, 0], [[1, 0], [0, 0.02]], size=50)
y1 = np.random.multivariate_normal([0, 0], [[0.02, 0], [0, 1]], size=50)
y2 = np.random.multivariate_normal([2, 2], [[1, -0.9], [-0.9, 1]], size=50)
y3 = np.random.multivariate_normal([-2, -2], [[0.1, 0], [0, 0.1]], size=50)
y = np.vstack([y0, y1, y2, y3])
bpplt.pyplot.plot(y[:,0], y[:,1], 'rx')
N = 200
D = 2
K = 10
alpha = Dirichlet(1e-5*np.ones(K),
name='alpha')
Z = Categorical(alpha,
plates=(N,),
name='z')
mu = Gaussian(np.zeros(D), 1e-5*np.identity(D),
plates=(K,),
name='mu')
Lambda = Wishart(D, 1e-5*np.identity(D),
plates=(K,),
name='Lambda')
Y = Mixture(Z, Gaussian, mu, Lambda,
name='Y')
Z.initialize_from_random()
Q = VB(Y, mu, Lambda, Z, alpha)
Y.observe(y)
Q.update(repeat=1000)
bpplt.gaussian_mixture_2d(Y, scale=2)
# Have to define these limits because on some particular environments these
# may otherwise differ and thus result in an image comparsion failure
bpplt.pyplot.xlim([-3, 6])
bpplt.pyplot.ylim([-3, 5])
def test_initialization(self):
"""
Test initialization of categorical nodes
"""
# Test initialization from random
with warnings.catch_warnings():
warnings.simplefilter("ignore", RuntimeWarning)
Z = Categorical([[0.0, 1.0, 0.0],
[0.0, 0.0, 1.0]])
Z.initialize_from_random()
u = Z._message_to_child()
self.assertAllClose(u[0],
[[0, 1, 0],
[0, 0, 1]])
pass
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_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
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 mixture_model(distribution, *args, K=3, N=100):
# Prior for state probabilities
alpha = Dirichlet(1e-3 * np.ones(K), name='alpha')
# Cluster assignments
Z = Categorical(alpha, plates=(N, ), name='Z')
# Observation distribution
Y = Mixture(Z, distribution, *args, name='Y')
Q = VB(Y, Z, alpha)
return Q
def test_moments(self):
"""
Test the moments of categorical nodes.
"""
# Simple test
X = Categorical([0.7,0.2,0.1])
u = X._message_to_child()
self.assertEqual(len(u), 1)
self.assertAllClose(u[0],
[0.7,0.2,0.1])
# Test plates in p
p = np.random.dirichlet([1,1], size=3)
X = Categorical(p)
u = X._message_to_child()
self.assertAllClose(u[0],
p)
# Test with Dirichlet prior
P = Dirichlet([7, 3])
logp = P._message_to_child()[0]
p0 = np.exp(logp[0]) / (np.exp(logp[0]) + np.exp(logp[1]))
p1 = np.exp(logp[1]) / (np.exp(logp[0]) + np.exp(logp[1]))
X = Categorical(P)
u = X._message_to_child()
p = np.array([p0, p1])
self.assertAllClose(u[0],
p)
# Test with broadcasted plates
P = Dirichlet([7, 3], plates=(10,))
X = Categorical(P)
u = X._message_to_child()
self.assertAllClose(u[0] * np.ones(X.get_shape(0)),
p*np.ones((10,1)))
pass
def test_gradient(self):
"""
Check the Euclidean gradient of the categorical node
"""
Z = Categorical([[0.3, 0.5, 0.2], [0.1, 0.6, 0.3]])
Y = Mixture(Z, Gamma, [2, 3, 4], [5, 6, 7])
Y.observe([4.2, 0.2])
def f(x):
Z.set_parameters([np.reshape(x, Z.get_shape(0))])
return Z.lower_bound_contribution() + Y.lower_bound_contribution()
def df(x):
Z.set_parameters([np.reshape(x, Z.get_shape(0))])
g = Z.get_riemannian_gradient()
return Z.get_gradient(g)[0]
x0 = np.ravel(np.log([[2, 3, 7], [0.1, 3, 1]]))
self.assertAllClose(
misc.gradient(f, x0),
np.ravel(df(x0))
)
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
import numpy numpy.random.seed(1) p0 = [0.1, 0.9, 0.1, 0.9, 0.1, 0.9, 0.1, 0.9, 0.1, 0.9] p1 = [0.1, 0.1, 0.1, 0.1, 0.1, 0.9, 0.9, 0.9, 0.9, 0.9] p2 = [0.9, 0.9, 0.9, 0.9, 0.9, 0.1, 0.1, 0.1, 0.1, 0.1] import numpy as np p = np.array([p0, p1, p2]) from bayespy.utils import random z = random.categorical([1 / 3, 1 / 3, 1 / 3], size=100) x = random.bernoulli(p[z]) N = 100 D = 10 K = 10 from bayespy.nodes import Categorical, Dirichlet R = Dirichlet(K * [1e-5], name='R') Z = Categorical(R, plates=(N, 1), name='Z') from bayespy.nodes import Beta P = Beta([0.5, 0.5], plates=(D, K), name='P') from bayespy.nodes import Mixture, Bernoulli X = Mixture(Z, Bernoulli, P) from bayespy.inference import VB Q = VB(Z, R, X, P) P.initialize_from_random() X.observe(x) Q.update(repeat=1000) import bayespy.plot as bpplt bpplt.hinton(P) bpplt.pyplot.show()
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
dietEnum[x[3]], lifeStyleEnum[x[4]], cholesterolEnum[x[5]],
heartDiseaseEnum[x[6]]
])
"""
data-->[[0, 0, 0, 1, 3, 0, 0], [0, 1, 0, 1, 3, 0, 0], [1, 0, 1, 0, 2, 1, 0],
[4, 0, 0, 1, 3, 2, 1],[3, 1, 0, 0, 0, 2, 1], [2, 0, 0, 1, 1, 0, 0], [4, 0, 0, 0, 2, 0, 0],
[0, 0, 0, 1, 3, 0, 0],[3, 1, 0, 0, 0, 2, 1], [1, 1, 1, 0, 0, 2, 0], [4, 1, 1, 1, 2, 0, 0]]
"""
data = np.array(data)
N = len(data)
print(N)
p_age = Dirichlet(
1.0 *
np.ones(5)) #used to classify text in a document to a particular topic.
age = Categorical(
p_age, plates=(N, )) #a sequence of unique values and no missing values
age.observe(data[:, 0])
p_gender = Dirichlet(1.0 * np.ones(2))
gender = Categorical(p_gender, plates=(N, ))
gender.observe(data[:, 1])
p_familyhistory = Dirichlet(1.0 * np.ones(2))
familyhistory = Categorical(p_familyhistory, plates=(N, ))
familyhistory.observe(data[:, 2])
p_diet = Dirichlet(1.0 * np.ones(3))
diet = Categorical(p_diet, plates=(N, ))
diet.observe(data[:, 3])
p_lifestyle = Dirichlet(1.0 * np.ones(4))
def test_moments(self):
"""
Test the moments of categorical nodes.
"""
# Simple test
X = Categorical([0.7, 0.2, 0.1])
u = X._message_to_child()
self.assertEqual(len(u), 1)
self.assertAllClose(u[0], [0.7, 0.2, 0.1])
# Test plates in p
p = np.random.dirichlet([1, 1], size=3)
X = Categorical(p)
u = X._message_to_child()
self.assertAllClose(u[0], p)
# Test with Dirichlet prior
P = Dirichlet([7, 3])
logp = P._message_to_child()[0]
p0 = np.exp(logp[0]) / (np.exp(logp[0]) + np.exp(logp[1]))
p1 = np.exp(logp[1]) / (np.exp(logp[0]) + np.exp(logp[1]))
X = Categorical(P)
u = X._message_to_child()
p = np.array([p0, p1])
self.assertAllClose(u[0], p)
# Test with broadcasted plates
P = Dirichlet([7, 3], plates=(10, ))
X = Categorical(P)
u = X._message_to_child()
self.assertAllClose(u[0] * np.ones(X.get_shape(0)), p * np.ones(
(10, 1)))
pass
'''
p0 = [0.1, 0.1, 0.1, 0.9, 0.9, 0.9, 0.1, 0.1, 0.1, 0.1]
p1 = [0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.9, 0.9, 0.9, 0.9]
p2 = [0.9, 0.9, 0.9, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1]
p = np.array([p0, p1, p2])
z = random.categorical([1/3, 1/3, 1/3], size=100)
x = random.bernoulli(p[z])
N = 100
D = 10
K = 3
R = Dirichlet(K*[1e-5],name='R')
Z = Categorical(R,plates=(N,1),name='Z')
P = Beta([0.5, 0.5],plates=(D,K),name='P')
X = Mixture(Z, Bernoulli, P)
Q = VB(Z, R, X, P)
P.initialize_from_random()
X.observe(x)
Q.update(repeat=1000)
#print(" P:")
#print( P.get_moments() )
#print(" R:")
#print( R.get_moments() )
from bayespy.nodes import Dirichlet, Categorical from bayespy.nodes import Gaussian, Wishart from bayespy.nodes import Mixture from bayespy.inference import VB y0 = np.random.multivariate_normal([0, 0], [[2, 0], [0, 0.1]], size=50) y1 = np.random.multivariate_normal([0, 0], [[0.1, 0], [0, 2]], size=50) y2 = np.random.multivariate_normal([2, 2], [[2, -1.5], [-1.5, 2]], size=50) y3 = np.random.multivariate_normal([-2, -2], [[0.5, 0], [0, 0.5]], size=50) y = np.vstack([y0, y1, y2, y3]) N = 200 D = 2 K = 10 alpha = Dirichlet(1e-5*np.ones(K), name='alpha') Z = Categorical(alpha, plates=(N,),name='z') mu = Gaussian(np.zeros(D),1e-5*np.identity(D),plates=(K,),name='mu') Lambda = Wishart(D,1e-5*np.identity(D),plates=(K,),name='Lambda') Y = Mixture(Z, Gaussian, mu, Lambda, name='Y') Z.initialize_from_random() Q = VB(Y, mu, Lambda, Z, alpha) Y.observe(y) Q.update(repeat=1000) bpplt.gaussian_mixture_2d(Y, alpha=alpha, scale=2)
from bayespy.nodes import Categorical, Mixture
from bayespy.inference import VB
import numpy as np
TRUE, FALSE = 1, 0
def _or(p_false, p_true):
return np.take([p_false, p_true], [[FALSE, TRUE], [TRUE, TRUE]], axis=0)
A = Categorical([0.5, 0.5])
T = Mixture(A, Categorical, [[0.99, 0.01], [0.8, 0.2]])
S = Categorical([0.5, 0.5])
L = Mixture(S, Categorical, [[0.98, 0.02], [0.75, 0.25]])
B = Mixture(S, Categorical, [[0.97, 0.03], [0.70, 0.30]])
X = Mixture(T, Mixture, L, Categorical, _or([0.96, 0.04], [0.115, 0.885]))
D = Mixture(B, Mixture, X, Categorical, _or([0.115, 0.885], [0.04, 0.96]))
T.observe(TRUE)
S.observe(FALSE)
B.observe(TRUE)
Q = VB(A, T, S, L, B, X, D)
def run(self, K=25, beta=0.5, alpha=0.00001, foci_thresh=0, num_neigh=4, hinton_plot=False, end=False):
'''Performs one run of the BBDP according to the specified parameters.'''
print("Transforming WCS participant data into binary vectors...")
x = u.transform_data_all(self.langs, norm=False, end=end, foci=True, foci_thresh=foci_thresh, num_neigh=num_neigh)
print("Finished transforming participant data")
self.participant_list = x[0]
N = len(x[0]) #number of data points (i.e. WCS participants)
D = np.shape(x[1])[1] #number of features
#K = 20 #number of initial clusters
R = Dirichlet(K*[alpha],
name='R')
Z = Categorical(R,
plates=(N,1),
name='Z')
P = Beta([beta, beta],
plates=(D,K),
name='P')
X = Mixture(Z, Bernoulli, P)
Q = VB(Z, R, X, P)
P.initialize_from_random()
X.observe(x[1])
Q.update(repeat=1000)
if hinton_plot:
bpplt.hinton(Z)
bpplt.pyplot.show()
bpplt.hinton(R)
bpplt.pyplot.show()
#Get the weight matrix stored in Z (weights determine which cluster data point belongs to)
z = Z._message_to_child()[0]
z = z * np.ones(Z.plates+(1,))
z = np.squeeze(z)
self.z = z
#Get the weights stored in R (proportional to the size of the clusters)
r = np.exp(R._message_to_child()[0])
r = r * np.ones(R.plates+(1,))
r = np.squeeze(r)
self.r = r
#Get the cluster assignment of each data point
self.c_assign = np.argmax(self.z, axis=1)
#Write cluster results to a file
if self.write_to_file:
if end:
save_path = "cluster_results_end_K={}_B={}_a={}_t={}_nn={}".format(K, beta, alpha, foci_thresh, num_neigh)
else:
save_path = "cluster_results_K={}_B={}_a={}_t={}_nn={}".format(K, beta, alpha, foci_thresh, num_neigh)
while path.exists(save_path+".txt"):
#save_path already exists
try:
old_file_num = int(save_path[save_path.find('(')+1:-1])
new_file_num = old_file_num + 1
save_path = save_path[0:save_path.find('(')] + '(' + str(new_file_num) + ')'
except ValueError:
save_path = save_path + " (1)"
self.save_path = save_path
file = open(path.abspath(self.save_path+".txt"), 'w')
#Write cluster assignment matrix Z (gives the probability that observation i belongs to cluster j)
if 'Z' not in self.in_file:
for i in range(len(self.z)):
line = "\t".join([str(x) for x in self.z[i]]) + "\n"
file.write(line)
file.write('---Z\n')
self.in_file.append('Z')
#Write cluster weights matrix R (proportional to the size of the resulting clusters)
if 'R' not in self.in_file:
line = "\t".join([str(x) for x in self.r]) + "\n"
file.write(line)
file.write('---R\n')
self.in_file.append('R')
#Write deterministic cluster assignments with the corresponding participant key
if 'C' not in self.in_file:
line1 = "\t".join([str(x) for x in self.participant_list]) + "\n"
line2 = "\t".join([str(x) for x in self.c_assign]) + "\n"
file.write(line1)
file.write(line2)
file.write('---C\n')
self.in_file.append('C')
file.close()
return self.c_assign
def run(N=500, seed=42, maxiter=100, plot=True):
"""
Run deterministic annealing demo for 1-D Gaussian mixture.
"""
if seed is not None:
np.random.seed(seed)
mu = GaussianARD(0, 1,
plates=(2,),
name='means')
Z = Categorical([0.3, 0.7],
plates=(N,),
name='classes')
Y = Mixture(Z, GaussianARD, mu, 1,
name='observations')
# Generate data
z = Z.random()
data = np.empty(N)
for n in range(N):
data[n] = [4, -4][z[n]]
Y.observe(data)
# Initialize means closer to the inferior local optimum in which the
# cluster means are swapped
mu.initialize_from_value([0, 6])
Q = VB(Y, Z, mu)
Q.save()
#
# Standard VB-EM algorithm
#
Q.update(repeat=maxiter)
mu_vbem = mu.u[0].copy()
L_vbem = Q.compute_lowerbound()
#
# VB-EM with deterministic annealing
#
Q.load()
beta = 0.01
while beta < 1.0:
beta = min(beta*1.2, 1.0)
print("Set annealing to %.2f" % beta)
Q.set_annealing(beta)
Q.update(repeat=maxiter, tol=1e-4)
mu_anneal = mu.u[0].copy()
L_anneal = Q.compute_lowerbound()
print("==============================")
print("RESULTS FOR VB-EM vs ANNEALING")
print("Fixed component probabilities:", np.array([0.3, 0.7]))
print("True component means:", np.array([4, -4]))
print("VB-EM component means:", mu_vbem)
print("VB-EM lower bound:", L_vbem)
print("Annealed VB-EM component means:", mu_anneal)
print("Annealed VB-EM lower bound:", L_anneal)
return
def test_observed(self):
"""
Test observed categorical nodes
"""
# Single observation
X = Categorical([0.7,0.2,0.1])
X.observe(2)
u = X._message_to_child()
self.assertAllClose(u[0],
[0,0,1])
# One plate axis
X = Categorical([0.7,0.2,0.1], plates=(2,))
X.observe([2,1])
u = X._message_to_child()
self.assertAllClose(u[0],
[[0,0,1],
[0,1,0]])
# Several plate axes
X = Categorical([0.7,0.1,0.1,0.1], plates=(2,3,))
X.observe([[2,1,1],
[0,2,3]])
u = X._message_to_child()
self.assertAllClose(u[0],
[ [[0,0,1,0],
[0,1,0,0],
[0,1,0,0]],
[[1,0,0,0],
[0,0,1,0],
[0,0,0,1]] ])
# Check invalid observations
X = Categorical([0.7,0.2,0.1])
self.assertRaises(ValueError,
X.observe,
-1)
self.assertRaises(ValueError,
X.observe,
3)
self.assertRaises(ValueError,
X.observe,
1.5)
pass
def generateCPD(
self, term
): #, X_train, y_train, X_test, y_test, X_validation, y_validation, g_train, g_test, g_validation):
clf = loadClf(self.ontology[term]['name'], self.fold, self.clfName)
posTrain = sum(clf.y_train == POSTIVE_LABEL)
negTrain = sum(clf.y_train == NEGATIVE_LABEL)
totalTrain = posTrain + negTrain
children = sorted(self.ontology[term]['children'])
parents = sorted(self.ontology[term]['parents'])
labels = {
l: PRIOR
for l in product(*((POSTIVE_LABEL, NEGATIVE_LABEL), ) *
(len(children) + 1))
}
if children:
childNodes = [
self.ontology[child]['node'][self.fold][self.clfName]
for child in children
]
for gene, y in zip(clf.g_train, clf.y_train):
event = []
for child in children:
event.append(POSTIVE_LABEL if gene in self.ontology.
associations[child] else NEGATIVE_LABEL)
event.append(POSTIVE_LABEL if gene in self.ontology.
associations[term] else NEGATIVE_LABEL)
assert (gene in self.ontology.associations[term]) == (
y == POSTIVE_LABEL)
event = tuple(event)
labels[event] += 1
def countBoth(event):
return labels[event[:-1] +
(POSTIVE_LABEL, )] + labels[event[:-1] +
(NEGATIVE_LABEL, )]
cprior = PRIOR * (2**len(children))
types = [Mixture] * (len(children) - 1) + [Categorical]
mixparams = [i for s in zip(childNodes, types) for i in s]
cpd = numpy.empty((2, ) * (len(children) + 1))
for event, counted in labels.items():
v = cpd
for b in event[:-1]:
v = v[b]
hid = event[-1]
print("Event: ", event)
if POSTIVE_LABEL not in event[:
-1]: # Všichni potomci označeni "ne"
v[hid] = counted / countBoth(event)
print("Stored %d / %d" % (counted, countBoth(event)))
else:
v[hid] = {POSTIVE_LABEL: 0.99, NEGATIVE_LABEL: 0.01}[hid]
print("Stored %d : %d" % (hid, v[hid]))
#print(term,"<-",",".join(children))
print(cpd)
#print(labels)
hidden = Mixture(*mixparams, cpd)
hidden.params = cpd
else: #No children
#hidden = DiscreteDistribution({'0': posTrain / totalTrain, '1': negTrain / totalTrain})
params = (posTrain / totalTrain, negTrain / totalTrain)
hidden = Categorical(params)
hidden.params = params
#print("Hidden node %s:" % term)
#print(repr(hidden))
#print([p for p in hidden.parents if isinstance(p, Stochastic)])
#print(hidden.get_moments())
conf = clf.conf + PRIOR
#posTest, negTest = numpy.sum(conf, 1)
posTest, negTest = numpy.sum(conf, 0)
#print("Confusion matrix:")
#print(conf)
try:
assert term != self.ontology.root
pos_decisions = clf.decision_function(
clf.X_test[clf.y_test == POSTIVE_LABEL])
neg_decisions = clf.decision_function(
clf.X_test[clf.y_test == NEGATIVE_LABEL])
means = [numpy.mean(pos_decisions)], [numpy.mean(neg_decisions)]
maxprec = 100.0
precs = [[numpy.min((1 / numpy.var(pos_decisions), maxprec))]
], [[numpy.min((1 / numpy.var(neg_decisions), maxprec))]]
#else:
except (ValueError, AssertionError):
means = [-1.], [1.]
precs = [[1.]], [[1.]]
print("Gaussian params:", term, self.ontology[term]['name'], means,
precs)
observed = Mixture(hidden, Gaussian, means, precs)
#observed = ConditionalProbabilityTable([
# ['0', '0', conf[0][0] / posTest], # if term != root else 1.],
# ['0', '1', conf[0][1] / posTest], # if term != root else 0.],
# ['1', '0', conf[1][0] / negTest], # if term != root else 0.],
# ['1', '1', conf[1][1] / negTest]], #if term != root else 1.]],
# [hidden.distribution])
#print("Observed node %s - %s:" % (term, self.ontology[term]['name']))
#print(repr(observed))
#print([p for p in observed.parents if isinstance(p, Stochastic)])
self.ontology[term]['node'][self.fold][self.clfName] = hidden
#self.ontology[term]['clf'][self.fold][self.clfName] = clf, X_validation, y_validation, g_validation
assert self.lenValidation is None or self.lenValidation == len(
clf.y_validation)
self.lenValidation = len(clf.y_validation)
self.allobserved[term] = observed
self.allhidden[term] = hidden
self.extranodes.update(
(p for p in hidden.parents if isinstance(p, Stochastic)))
def test_init(self):
"""
Test the creation of Gate node
"""
# Gating scalar node
Z = Categorical(np.ones(3) / 3)
X = GaussianARD(0, 1, shape=(), plates=(3, ))
Y = Gate(Z, X)
self.assertEqual(Y.plates, ())
self.assertEqual(Y.dims, ((), ()))
# Gating non-scalar node
Z = Categorical(np.ones(3) / 3)
X = GaussianARD(0, 1, shape=(2, ), plates=(3, ))
Y = Gate(Z, X)
self.assertEqual(Y.plates, ())
self.assertEqual(Y.dims, ((2, ), (2, 2)))
# Plates from Z
Z = Categorical(np.ones(3) / 3, plates=(4, ))
X = GaussianARD(0, 1, shape=(2, ), plates=(3, ))
Y = Gate(Z, X)
self.assertEqual(Y.plates, (4, ))
self.assertEqual(Y.dims, ((2, ), (2, 2)))
# Plates from X
Z = Categorical(np.ones(3) / 3)
X = GaussianARD(0, 1, shape=(2, ), plates=(4, 3))
Y = Gate(Z, X)
self.assertEqual(Y.plates, (4, ))
self.assertEqual(Y.dims, ((2, ), (2, 2)))
# Plates from Z and X
Z = Categorical(np.ones(3) / 3, plates=(5, ))
X = GaussianARD(0, 1, shape=(2, ), plates=(4, 1, 3))
Y = Gate(Z, X)
self.assertEqual(Y.plates, (4, 5))
self.assertEqual(Y.dims, ((2, ), (2, 2)))
# Gating non-default plate
Z = Categorical(np.ones(3) / 3)
X = GaussianARD(0, 1, shape=(), plates=(3, 4))
Y = Gate(Z, X, gated_plate=-2)
self.assertEqual(Y.plates, (4, ))
self.assertEqual(Y.dims, ((), ()))
# Fixed gating
Z = 2
X = GaussianARD(0, 1, shape=(2, ), plates=(3, ))
Y = Gate(Z, X)
self.assertEqual(Y.plates, ())
self.assertEqual(Y.dims, ((2, ), (2, 2)))
# Fixed X
Z = Categorical(np.ones(3) / 3)
X = [1, 2, 3]
Y = Gate(Z, X, moments=GaussianMoments(0))
self.assertEqual(Y.plates, ())
self.assertEqual(Y.dims, ((), ()))
# Do not accept non-negative cluster plates
Z = Categorical(np.ones(3) / 3)
X = GaussianARD(0, 1, plates=(3, ))
self.assertRaises(ValueError, Gate, Z, X, gated_plate=0)
# None of the parents have the cluster plate axis
Z = Categorical(np.ones(3) / 3)
X = GaussianARD(0, 1)
self.assertRaises(ValueError, Gate, Z, X)
# Inconsistent cluster plate
Z = Categorical(np.ones(3) / 3)
X = GaussianARD(0, 1, plates=(2, ))
self.assertRaises(ValueError, Gate, Z, X)
pass
def test_message_to_parent(self):
"""
Test the message to parents of Gate node.
"""
# Unobserved and broadcasting
Z = 2
X = GaussianARD(0, 1, shape=(), plates=(3, ))
F = Gate(Z, X)
Y = GaussianARD(F, 1)
m = F._message_to_parent(0)
self.assertEqual(len(m), 1)
self.assertAllClose(m[0], 0 * np.ones(3))
m = F._message_to_parent(1)
self.assertEqual(len(m), 2)
self.assertAllClose(m[0] * np.ones(3), [0, 0, 0])
self.assertAllClose(m[1] * np.ones(3), [0, 0, 0])
# Gating scalar node
Z = 2
X = GaussianARD([1, 2, 3], 1, shape=(), plates=(3, ))
F = Gate(Z, X)
Y = GaussianARD(F, 1)
Y.observe(10)
m = F._message_to_parent(0)
self.assertAllClose(
m[0], [10 * 1 - 0.5 * 2, 10 * 2 - 0.5 * 5, 10 * 3 - 0.5 * 10])
m = F._message_to_parent(1)
self.assertAllClose(m[0], [0, 0, 10])
self.assertAllClose(m[1], [0, 0, -0.5])
# Fixed X
Z = 2
X = [1, 2, 3]
F = Gate(Z, X, moments=GaussianMoments(0))
Y = GaussianARD(F, 1)
Y.observe(10)
m = F._message_to_parent(0)
self.assertAllClose(
m[0], [10 * 1 - 0.5 * 1, 10 * 2 - 0.5 * 4, 10 * 3 - 0.5 * 9])
m = F._message_to_parent(1)
self.assertAllClose(m[0], [0, 0, 10])
self.assertAllClose(m[1], [0, 0, -0.5])
# Uncertain gating
Z = Categorical([0.2, 0.3, 0.5])
X = GaussianARD([1, 2, 3], 1, shape=(), plates=(3, ))
F = Gate(Z, X)
Y = GaussianARD(F, 1)
Y.observe(10)
m = F._message_to_parent(0)
self.assertAllClose(
m[0], [10 * 1 - 0.5 * 2, 10 * 2 - 0.5 * 5, 10 * 3 - 0.5 * 10])
m = F._message_to_parent(1)
self.assertAllClose(m[0], [0.2 * 10, 0.3 * 10, 0.5 * 10])
self.assertAllClose(m[1], [-0.5 * 0.2, -0.5 * 0.3, -0.5 * 0.5])
# Plates in Z
Z = [2, 0]
X = GaussianARD([1, 2, 3], 1, shape=(), plates=(3, ))
F = Gate(Z, X)
Y = GaussianARD(F, 1)
Y.observe([10, 20])
m = F._message_to_parent(0)
self.assertAllClose(
m[0], [[10 * 1 - 0.5 * 2, 10 * 2 - 0.5 * 5, 10 * 3 - 0.5 * 10],
[20 * 1 - 0.5 * 2, 20 * 2 - 0.5 * 5, 20 * 3 - 0.5 * 10]])
m = F._message_to_parent(1)
self.assertAllClose(m[0], [20, 0, 10])
self.assertAllClose(m[1], [-0.5, 0, -0.5])
# Plates in X
Z = 2
X = GaussianARD([[1, 2, 3], [4, 5, 6]], 1, shape=(), plates=(
2,
3,
))
F = Gate(Z, X)
Y = GaussianARD(F, 1)
Y.observe([10, 20])
m = F._message_to_parent(0)
self.assertAllClose(m[0], [
10 * 1 - 0.5 * 2 + 20 * 4 - 0.5 * 17, 10 * 2 - 0.5 * 5 + 20 * 5 -
0.5 * 26, 10 * 3 - 0.5 * 10 + 20 * 6 - 0.5 * 37
])
m = F._message_to_parent(1)
self.assertAllClose(m[0], [[0, 0, 10], [0, 0, 20]])
self.assertAllClose(m[1] * np.ones((2, 3)),
[[0, 0, -0.5], [0, 0, -0.5]])
# Gating non-default plate
Z = 2
X = GaussianARD([[1], [2], [3]], 1, shape=(), plates=(3, 1))
F = Gate(Z, X, gated_plate=-2)
Y = GaussianARD(F, 1)
Y.observe([10])
m = F._message_to_parent(0)
self.assertAllClose(
m[0], [10 * 1 - 0.5 * 2, 10 * 2 - 0.5 * 5, 10 * 3 - 0.5 * 10])
m = F._message_to_parent(1)
self.assertAllClose(m[0], [[0], [0], [10]])
self.assertAllClose(m[1], [[0], [0], [-0.5]])
# Gating non-scalar node
Z = 2
X = GaussianARD([[1, 4], [2, 5], [3, 6]], 1, shape=(2, ), plates=(3, ))
F = Gate(Z, X)
Y = GaussianARD(F, 1)
Y.observe([10, 20])
m = F._message_to_parent(0)
self.assertAllClose(m[0], [
10 * 1 - 0.5 * 2 + 20 * 4 - 0.5 * 17, 10 * 2 - 0.5 * 5 + 20 * 5 -
0.5 * 26, 10 * 3 - 0.5 * 10 + 20 * 6 - 0.5 * 37
])
m = F._message_to_parent(1)
I = np.identity(2)
self.assertAllClose(m[0], [[0, 0], [0, 0], [10, 20]])
self.assertAllClose(m[1], [0 * I, 0 * I, -0.5 * I])
# Broadcasting the moments on the cluster axis
Z = 2
X = GaussianARD(2, 1, shape=(), plates=(3, ))
F = Gate(Z, X)
Y = GaussianARD(F, 1)
Y.observe(10)
m = F._message_to_parent(0)
self.assertAllClose(
m[0], [10 * 2 - 0.5 * 5, 10 * 2 - 0.5 * 5, 10 * 2 - 0.5 * 5])
m = F._message_to_parent(1)
self.assertAllClose(m[0], [0, 0, 10])
self.assertAllClose(m[1], [0, 0, -0.5])
pass
import numpy as np
with open('7-dataset.csv') as f:
dataset = np.array(list(reader(f)))
enum = [list(set(column)) for column in dataset.T]
dataset = np.array([[enum[i].index(j) for i, j in enumerate(row)]
for row in dataset])
n = len(dataset)
categoricals = []
for i in range(len(enum) - 1):
dirichlet = Dirichlet(np.ones(len(enum[i])))
categoricals.append(Categorical(dirichlet, plates=(n, )))
categoricals[i].observe(dataset[:, i])
target = Dirichlet(np.ones(2), plates=tuple([len(x) for x in enum[:-1]]))
model = MultiMixture(categoricals, Categorical, target)
model.observe(dataset[:, -1])
target.update()
while True:
tup = [
enum[i].index(j) for i, j in enumerate(input('Tuple : ').split(','))
]
result = MultiMixture(tup, Categorical,
target).get_moments()[0][enum[-1].index("Y")]
print(result)
elif myRole == self.roles[0]:
p = [0,2/3,1/3]
elif myRole == self.roles[1]:
p = [1/3,1/3,1/3]
else:
p = [1/2,2/3,0]
elif numPlayers == 6:
if myRole == self.roles[3]:
p = [1/5, 3/5, 1/5]
elif myRole == self.roles[0]:
p = [0, 3/4, 1/4]
elif myRole == self.roles[2]:
p = [1/4, 2/4, 1/4]
else:
p = [1/4, 3/4, 0]
else:
if myRole == self.roles[0]:
p = [1/6, 3/6, 2/6]
elif myRole == self.roles[1]:
p = [0, 3/5, 2/5]
elif myRole == self.roles[2]:
p = [1/5, 2/5, 2/5]
else:
p = [1/5, 3/5, 1/5]
return Categorical(p)
def shotProbs(self,):
def test_observed(self):
"""
Test observed categorical nodes
"""
# Single observation
X = Categorical([0.7, 0.2, 0.1])
X.observe(2)
u = X._message_to_child()
self.assertAllClose(u[0], [0, 0, 1])
# One plate axis
X = Categorical([0.7, 0.2, 0.1], plates=(2, ))
X.observe([2, 1])
u = X._message_to_child()
self.assertAllClose(u[0], [[0, 0, 1], [0, 1, 0]])
# Several plate axes
X = Categorical([0.7, 0.1, 0.1, 0.1], plates=(
2,
3,
))
X.observe([[2, 1, 1], [0, 2, 3]])
u = X._message_to_child()
self.assertAllClose(u[0], [[[0, 0, 1, 0], [0, 1, 0, 0], [0, 1, 0, 0]],
[[1, 0, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]]])
# Check invalid observations
X = Categorical([0.7, 0.2, 0.1])
self.assertRaises(ValueError, X.observe, -1)
self.assertRaises(ValueError, X.observe, 3)
self.assertRaises(ValueError, X.observe, 1.5)
pass
# NOTE: Python's built-in booleans don't work nicely for indexing, thus define
# own variables:
FALSE = 0
TRUE = 1
def _or(p_false, p_true):
"""
Build probability table for OR-operation of two parents
p_false: Probability table to use if both are FALSE
p_true: Probability table to use if one or both is TRUE
"""
return np.take([p_false, p_true], [[FALSE, TRUE], [TRUE, TRUE]], axis=0)
asia = Categorical([0.5, 0.5])
tuberculosis = Mixture(asia, Categorical, [[0.99, 0.01], [0.8, 0.2]])
smoking = Categorical([0.5, 0.5])
lung = Mixture(smoking, Categorical, [[0.98, 0.02], [0.25, 0.75]])
bronchitis = Mixture(smoking, Categorical, [[0.97, 0.03], [0.08, 0.92]])
xray = Mixture(tuberculosis, Mixture, lung, Categorical,
_or([0.96, 0.04], [0.115, 0.885]))
dyspnea = Mixture(bronchitis, Mixture, tuberculosis, Mixture, lung, Categorical,
[_or([0.6, 0.4], [0.18, 0.82]),
_or([0.11, 0.89], [0.04, 0.96])])
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
def run(N=100000, N_batch=50, seed=42, maxiter=100, plot=True):
"""
Run deterministic annealing demo for 1-D Gaussian mixture.
"""
if seed is not None:
np.random.seed(seed)
# Number of clusters in the model
K = 20
# Dimensionality of the data
D = 5
# Generate data
K_true = 10
spread = 5
means = spread * np.random.randn(K_true, D)
z = random.categorical(np.ones(K_true), size=N)
data = np.empty((N, D))
for n in range(N):
data[n] = means[z[n]] + np.random.randn(D)
#
# Standard VB-EM algorithm
#
# Full model
mu = Gaussian(np.zeros(D), np.identity(D), plates=(K, ), name='means')
alpha = Dirichlet(np.ones(K), name='class probabilities')
Z = Categorical(alpha, plates=(N, ), name='classes')
Y = Mixture(Z, Gaussian, mu, np.identity(D), name='observations')
# Break symmetry with random initialization of the means
mu.initialize_from_random()
# Put the data in
Y.observe(data)
# Run inference
Q = VB(Y, Z, mu, alpha)
Q.save(mu)
Q.update(repeat=maxiter)
if plot:
bpplt.pyplot.plot(np.cumsum(Q.cputime), Q.L, 'k-')
max_cputime = np.sum(Q.cputime[~np.isnan(Q.cputime)])
#
# Stochastic variational inference
#
# Construct smaller model (size of the mini-batch)
mu = Gaussian(np.zeros(D), np.identity(D), plates=(K, ), name='means')
alpha = Dirichlet(np.ones(K), name='class probabilities')
Z = Categorical(alpha,
plates=(N_batch, ),
plates_multiplier=(N / N_batch, ),
name='classes')
Y = Mixture(Z, Gaussian, mu, np.identity(D), name='observations')
# Break symmetry with random initialization of the means
mu.initialize_from_random()
# Inference engine
Q = VB(Y, Z, mu, alpha, autosave_filename=Q.autosave_filename)
Q.load(mu)
# Because using mini-batches, messages need to be multiplied appropriately
print("Stochastic variational inference...")
Q.ignore_bound_checks = True
maxiter *= int(N / N_batch)
delay = 1
forgetting_rate = 0.7
for n in range(maxiter):
# Observe a mini-batch
subset = np.random.choice(N, N_batch)
Y.observe(data[subset, :])
# Learn intermediate variables
Q.update(Z)
# Set step length
step = (n + delay)**(-forgetting_rate)
# Stochastic gradient for the global variables
Q.gradient_step(mu, alpha, scale=step)
if np.sum(Q.cputime[:n]) > max_cputime:
break
if plot:
bpplt.pyplot.plot(np.cumsum(Q.cputime), Q.L, 'r:')
bpplt.pyplot.xlabel('CPU time (in seconds)')
bpplt.pyplot.ylabel('VB lower bound')
bpplt.pyplot.legend(['VB-EM', 'Stochastic inference'],
loc='lower right')
bpplt.pyplot.title('VB for Gaussian mixture model')
return
FALSE = 0
TRUE = 1
def _or(p_false, p_true):
"""
Build probability table for OR-operation of two parents
p_false: Probability table to use if both are FALSE
p_true: Probability table to use if one or both is TRUE
"""
return np.take([p_false, p_true], [[FALSE, TRUE], [TRUE, TRUE]], axis=0)
asia = Categorical([0.5, 0.5])
tuberculosis = Mixture(asia, Categorical, [[0.99, 0.01], [0.8, 0.2]])
smoking = Categorical([0.5, 0.5])
lung = Mixture(smoking, Categorical, [[0.98, 0.02], [0.25, 0.75]])
bronchitis = Mixture(smoking, Categorical, [[0.97, 0.03], [0.08, 0.92]])
xray = Mixture(tuberculosis, Mixture, lung, Categorical,
_or([0.96, 0.04], [0.115, 0.885]))
dyspnea = Mixture(
bronchitis, Mixture, tuberculosis, Mixture, lung, Categorical,
[_or([0.6, 0.4], [0.18, 0.82]),
def test_message_to_child(self):
"""
Test the message to child of Gate node.
"""
# Gating scalar node
Z = 2
X = GaussianARD([1, 2, 3], 1, shape=(), plates=(3, ))
Y = Gate(Z, X)
u = Y._message_to_child()
self.assertEqual(len(u), 2)
self.assertAllClose(u[0], 3)
self.assertAllClose(u[1], 3**2 + 1)
# Fixed X
Z = 2
X = [1, 2, 3]
Y = Gate(Z, X, moments=GaussianMoments(0))
u = Y._message_to_child()
self.assertEqual(len(u), 2)
self.assertAllClose(u[0], 3)
self.assertAllClose(u[1], 3**2)
# Uncertain gating
Z = Categorical([0.2, 0.3, 0.5])
X = GaussianARD([1, 2, 3], 1, shape=(), plates=(3, ))
Y = Gate(Z, X)
u = Y._message_to_child()
self.assertAllClose(u[0], 0.2 * 1 + 0.3 * 2 + 0.5 * 3)
self.assertAllClose(u[1], 0.2 * 2 + 0.3 * 5 + 0.5 * 10)
# Plates in Z
Z = [2, 0]
X = GaussianARD([1, 2, 3], 1, shape=(), plates=(3, ))
Y = Gate(Z, X)
u = Y._message_to_child()
self.assertAllClose(u[0], [3, 1])
self.assertAllClose(u[1], [10, 2])
# Plates in X
Z = 2
X = GaussianARD([1, 2, 3], 1, shape=(), plates=(
4,
3,
))
Y = Gate(Z, X)
u = Y._message_to_child()
self.assertAllClose(np.ones(4) * u[0], np.ones(4) * 3)
self.assertAllClose(np.ones(4) * u[1], np.ones(4) * 10)
# Gating non-default plate
Z = 2
X = GaussianARD([[1], [2], [3]], 1, shape=(), plates=(3, 4))
Y = Gate(Z, X, gated_plate=-2)
u = Y._message_to_child()
self.assertAllClose(np.ones(4) * u[0], np.ones(4) * 3)
self.assertAllClose(np.ones(4) * u[1], np.ones(4) * 10)
# Gating non-scalar node
Z = 2
X = GaussianARD([1 * np.ones(4), 2 * np.ones(4), 3 * np.ones(4)],
1,
shape=(4, ),
plates=(3, ))
Y = Gate(Z, X)
u = Y._message_to_child()
self.assertAllClose(u[0], 3 * np.ones(4))
self.assertAllClose(u[1], 9 * np.ones((4, 4)) + 1 * np.identity(4))
# Broadcasting the moments on the cluster axis
Z = 2
X = GaussianARD(1, 1, shape=(), plates=(3, ))
Y = Gate(Z, X)
u = Y._message_to_child()
self.assertEqual(len(u), 2)
self.assertAllClose(u[0], 1)
self.assertAllClose(u[1], 1**2 + 1)
pass
