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 _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 _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_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_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_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_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 _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)
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()
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() )
print(" Z:")
print( Z.get_moments() )
print(" X:")
print( X.get_moments() )
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
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])])
# Mark observations
tuberculosis.observe(TRUE)
smoking.observe(FALSE)
bronchitis.observe(TRUE) # not a "chance" observation as in the original example
# Run inference
Q = VB(dyspnea, xray, bronchitis, lung, smoking, tuberculosis, asia)
Q.update(repeat=100)
# Show results
print("P(asia):", asia.get_moments()[0][TRUE])
print("P(tuberculosis):", tuberculosis.get_moments()[0][TRUE])
print("P(smoking):", smoking.get_moments()[0][TRUE])
print("P(lung):", lung.get_moments()[0][TRUE])
print("P(bronchitis):", bronchitis.get_moments()[0][TRUE])
print("P(xray):", xray.get_moments()[0][TRUE])
print("P(dyspnea):", dyspnea.get_moments()[0][TRUE])
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 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
from bayespy.nodes import Gaussian, Wishart
mui = Gaussian(np.zeros(D), 1e-5 * np.identity(D), plates=(K, ), name='mui')
Lambdai = Wishart(D, 1e-5 * np.identity(D), plates=(K, ), name='Lambdai')
from bayespy.nodes import Mixture
Y = Mixture(Zi, Gaussian, mui, Lambdai, name='Y')
Zi.initialize_from_random()
from bayespy.inference import VB
Q = VB(Y, mui, Lambdai, Zi, alpha)
Y.observe(np.reshape(C_mat, (-1, 2)))
Q.update(repeat=10)
#%%
K = 5 #hyperparameter
neta = 1e-6 * np.ones(K) #hyperparameter
print(neta.shape)
print(neta)
PI = bayespy.nodes.Dirichlet(neta, name='PI')
#%%
Z = bayespy.nodes.Categorical(PI, plates=(m, n, K), name='Z')
mean_vec = np.zeros(d) # to be initialized accorinding to image
precission_mat = 1e-5 * np.identity(
d) # to be initialized accorinding to image
mu = bayespy.nodes.Gaussian(mean_vec, precission_mat, plates=(K, ), name='U')
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 get_community_assignments_by(self,
method=None,
temp_dfile_file="gibbsldapp.dfile",
params={}):
if method == "HMM":
"""
model = hmm.MultinomialHMM(n_components=3)
model.startprob_ = np.array([0.6, 0.3, 0.1])
model.transmat_ = np.array([[0.7, 0.2, 0.1],
[0.3, 0.5, 0.2],
[0.3, 0.3, 0.4]])
model.emissionprob_ = np.array([[0.4, 0.2, 0.1, 0.3],
[0.3, 0.4, 0.1, 0.2],
[0.1, 0.3, 0.5, 0.1]])
X, Z = model.sample(1000)
print(np.asarray(X).T)
print(Z)
"""
"""
remodel = hmm.MultinomialHMM(n_components=3, n_iter=100)
remodel.fit(X)
Z2 = remodel.predict(X)
print(Z2)
"""
"""
seqs = []
lens = []
for walk in self._walks:
s = [[int(w)-1] for w in walk]
seqs.extend(s)
lens.append(len(s))
model = hmm.MultinomialHMM(n_components=params['number_of_topics'], tol=0.001, n_iter=5000)
model.fit(seqs, lens)
posteriors = model.predict_proba(np.asarray([[i] for i in range(self.g.number_of_nodes())]))
comms = np.argmax(posteriors, 1)
node2comm = {}
for id in range(len(comms)):
node2comm[str(id+1)] = comms[id]
return node2comm
"""
seqs = []
lens = []
for walk in self._walks:
s = [int(w) - 1 for w in walk]
seqs.append(s)
lens.append(len(s))
pipi = np.asarray([0.5, 0.5], dtype=np.float)
AA = np.asarray([[0.2, 0.8], [0.5, 0.5]], dtype=np.float)
OO = np.asarray([[0.9, 0.05, 0.05], [0.05, 0.05, 0.9]],
dtype=np.float)
seqs = []
for i in range(31):
seq = []
s = np.random.choice(range(2), p=pipi)
o = np.random.choice(range(3), p=OO[s, :])
seq.append(o)
for _ in range(59):
s = np.random.choice(range(2), p=AA[s, :])
o = np.random.choice(range(3), p=OO[s, :])
seq.append(o)
seqs.append(seq)
seqs = np.vstack(seqs)
#print(seqs)
from bayespy.nodes import Categorical, Mixture
from bayespy.nodes import CategoricalMarkovChain
from bayespy.nodes import Dirichlet
from bayespy.inference import VB
K = params['number_of_topics'] # the number of hidden states
N = self.g.number_of_nodes() # the number of observations
#p0 = np.ones(K) / K
D = 31 #len(lens)
states = 60
a0 = Dirichlet(1e+1 * np.ones(K), plates=())
A = Dirichlet(1e+1 * np.ones(K), plates=(2, ), name='A')
P = Dirichlet(1e+1 * np.ones((K, N)))
Z = CategoricalMarkovChain(a0, A, states=states, plates=(D, ))
Y = Mixture(Z, Categorical, P)
Y.observe(seqs)
#a0.random()
#A.random()
#P.random()
Ainit = np.random.random((2, 2))
Ainit = np.divide(Ainit.T, np.sum(Ainit, 1)).T
#A.initialize_from_value(Ainit)
#print(Ainit)
Q = VB(Y, Z, P, A, a0)
Q.update(repeat=1000, plot=False, verbose=True)
#print(Z.random())
print(Q['A'])
return {}
if method == "LDA":
# Run GibbsLDA++
lda_exe_path = c._GIBBSLDA_PATH
if not os.path.exists(lda_exe_path):
raise ValueError("Invalid path of GibbsLDA++!")
temp_lda_folder = "./temp"
if not os.path.exists(temp_lda_folder):
os.makedirs(temp_lda_folder)
temp_dfile_path = os.path.join(temp_lda_folder, temp_dfile_file)
if not os.path.exists(temp_dfile_path):
# Save the walks into the dfile
n = len(self._walks)
with open(temp_dfile_path, 'w') as f:
f.write("{}\n".format(n))
for walk in self._walks:
f.write("{}\n".format(" ".join(str(w) for w in walk)))
initial_time = time.time()
cmd = "{} -est ".format(lda_exe_path)
cmd += "-alpha {} ".format(params['lda_alpha'])
cmd += "-beta {} ".format(params['lda_beta'])
cmd += "-ntopics {} ".format(params['number_of_topics'])
cmd += "-niters {} ".format(params['lda_number_of_iters'])
cmd += "-savestep {} ".format(params['lda_number_of_iters'] + 1)
cmd += "-dfile {} ".format(temp_dfile_path)
os.system(cmd)
print(
"-> The LDA algorithm run in {:.2f} secs".format(time.time() -
initial_time))
# Read wordmap file
id2node = {}
temp_wordmap_path = os.path.join(temp_lda_folder, "wordmap.txt")
with open(temp_wordmap_path, 'r') as f:
f.readline() # skip the first line
for line in f.readlines():
tokens = line.strip().split()
id2node[int(tokens[1])] = tokens[0]
# Read phi file
phi = np.zeros(shape=(params['number_of_topics'], len(id2node)),
dtype=np.float)
temp_phi_path = os.path.join(temp_lda_folder, "model-final.phi")
with open(temp_phi_path, 'r') as f:
for topicId, line in enumerate(f.readlines()):
phi[topicId, :] = [
float(value) for value in line.strip().split()
]
max_topics = np.argmax(phi, axis=0)
node2comm = {}
for nodeId in id2node:
node2comm[id2node[nodeId]] = max_topics[int(nodeId)]
return node2comm
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)
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
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)
Q.update(repeat=100)
print("P(asia): ", A.get_moments()[0][TRUE])
print("P(tuberculosis): ", T.get_moments()[0][TRUE])
print("P(smoking): ", S.get_moments()[0][TRUE])
print("P(lung): ", L.get_moments()[0][TRUE])
print("P(bronchitis): ", B.get_moments()[0][TRUE])
print("P(xray): ", X.get_moments()[0][TRUE])
print("P(dyspnea): ", D.get_moments()[0][TRUE])
def _or(p_false, p_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])])
tuberculosis.observe(TRUE)
smoking.observe(FALSE)
bronchitis.observe(TRUE)
Q = VB(dyspnea, xray, bronchitis, lung, smoking, tuberculosis, asia)
Q.update(repeat=100)
print("P(asia):", asia.get_moments()[0][TRUE])
print("P(tuberculosis):", tuberculosis.get_moments()[0][TRUE])
print("P(smoking):", smoking.get_moments()[0][TRUE])
print("P(lung):", lung.get_moments()[0][TRUE])
print("P(bronchitis):", bronchitis.get_moments()[0][TRUE])
print("P(xray):", xray.get_moments()[0][TRUE])
print("P(dyspnea):", dyspnea.get_moments()[0][TRUE])
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])])
# Mark observations
tuberculosis.observe(TRUE)
smoking.observe(FALSE)
bronchitis.observe(
TRUE) # not a "chance" observation as in the original example
# Run inference
Q = VB(dyspnea, xray, bronchitis, lung, smoking, tuberculosis, asia)
Q.update(repeat=100)
# Show results
print("P(asia):", asia.get_moments()[0][TRUE])
print("P(tuberculosis):", tuberculosis.get_moments()[0][TRUE])
print("P(smoking):", smoking.get_moments()[0][TRUE])
print("P(lung):", lung.get_moments()[0][TRUE])
print("P(bronchitis):", bronchitis.get_moments()[0][TRUE])
print("P(xray):", xray.get_moments()[0][TRUE])
import numpy
numpy.random.seed(1)
from bayespy.nodes import CategoricalMarkovChain
a0 = [0.6, 0.4] # p(rainy)=0.6, p(sunny)=0.4
A = [[0.7, 0.3], # p(rainy->rainy)=0.7, p(rainy->sunny)=0.3
[0.4, 0.6]] # p(sunny->rainy)=0.4, p(sunny->sunny)=0.6
N = 100
Z = CategoricalMarkovChain(a0, A, states=N)
from bayespy.nodes import Categorical, Mixture
P = [[0.1, 0.4, 0.5],
[0.6, 0.3, 0.1]]
Y = Mixture(Z, Categorical, P)
weather = Z.random()
activity = Mixture(weather, Categorical, P).random()
Y.observe(activity)
from bayespy.inference import VB
Q = VB(Y, Z)
Q.update()
import bayespy.plot as bpplt
bpplt.plot(Z)
bpplt.plot(1-weather, color='r', marker='x')
bpplt.pyplot.show()
