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
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
