from edward.stats import norm
from edward.variationals import Variational, Normal
class NormalPosterior:
"""
p(x, z) = p(z) = p(z | x) = Normal(z; mu, std)
"""
def __init__(self, mu, std):
self.mu = mu
self.std = std
self.num_vars = 1
def log_prob(self, xs, zs):
return tf.pack([norm.logpdf(z, self.mu, self.std) for z in tf.unpack(zs)])
ed.set_seed(42)
mu = tf.constant(1.0)
std = tf.constant(1.0)
model = NormalPosterior(mu, std)
variational = Variational()
variational.add(Normal(model.num_vars))
inference = ed.MFVI(model, variational)
sess = inference.initialize()
for t in range(1000):
loss = inference.update(sess)
inference.print_progress(t, loss, sess)
Posterior: (1-dimensional) Bernoulli
Variational model
Likelihood: Mean-field Bernoulli
"""
import edward as ed
import tensorflow as tf
from edward.stats import bernoulli
from edward.variationals import Variational, Bernoulli
class BernoulliPosterior:
"""
p(x, z) = p(z) = p(z | x) = Bernoulli(z; p)
"""
def __init__(self, p):
self.p = p
def log_prob(self, xs, zs):
return bernoulli.logpmf(zs, p)
ed.set_seed(42)
p = tf.constant(0.6)
model = BernoulliPosterior(p)
variational = Variational()
variational.add(Bernoulli(1))
inference = ed.MFVI(model, variational)
inference.run(n_iter=10000)
for j in xrange(self.N):
if j == i:
mat[i, i] = self.kernel_xy(xi, xi, sess)
else:
sij = self.kernel_xy(xi, xs[j, 1:], sess)
mat[i, j] = sij
sess.close()
return tf.constant(mat, dtype=tf.float32)
def log_prob(self, xs, zs):
K = self.kernel(xs)
log_prior = multivariate_normal.logpdf(zs[:, :], cov=K)
log_lik = tf.pack([tf.reduce_sum( \
bernoulli.logpmf(xs[:,0], self.inverse_link(tf.mul(xs[:,0], z))) \
) for z in tf.unpack(zs)])
return log_prior + log_lik
ed.set_seed(42)
# Data must have labels in the first column and features in
# subsequent columns.
df = np.loadtxt('data/crabs_train.txt', dtype='float32', delimiter=',')
data = ed.Data(tf.constant(df, dtype=tf.float32))
model = GaussianProcess(N=len(df))
variational = Variational()
variational.add(Normal(model.num_vars))
inference = ed.MFVI(model, variational, data)
inference.run(n_iter=10000)
Prior: Beta
Likelihood: Bernoulli
Variational model
Likelihood: Mean-field Beta
"""
import edward as ed
from edward.variationals import Variational, Beta
model_code = """
data {
int<lower=0> N;
int<lower=0,upper=1> y[N];
}
parameters {
real<lower=0,upper=1> theta;
}
model {
theta ~ beta(1.0, 1.0);
for (n in 1:N)
y[n] ~ bernoulli(theta);
}
"""
ed.set_seed(42)
model = ed.StanModel(model_code=model_code)
variational = Variational()
variational.add(Beta(1))
data = ed.Data(dict(N=10, y=[0, 1, 0, 0, 0, 0, 0, 0, 0, 1]))
inference = ed.MFVI(model, variational, data)
inference.run(n_iter=10000)
for k in xrange(self.K):
log_prior += norm.logpdf(mus[k*self.D], 0, np.sqrt(self.c))
log_prior += norm.logpdf(mus[k*self.D+1], 0, np.sqrt(self.c))
log_prior += invgamma.logpdf(sigmas[k*self.D], self.a, self.b)
log_prior += invgamma.logpdf(sigmas[k*self.D+1], self.a, self.b)
log_lik = tf.constant(0.0, dtype=tf.float32)
for x in tf.unpack(xs):
for k in xrange(self.K):
log_lik += tf.log(pi[k])
log_lik += multivariate_normal.logpdf(x,
mus[(k*self.D):((k+1)*self.D)],
sigmas[(k*self.D):((k+1)*self.D)])
log_prob += [log_prior + log_lik]
return tf.pack(log_prob)
ed.set_seed(42)
x = np.loadtxt('data/mixture_data.txt', dtype='float32', delimiter=',')
data = ed.Data(tf.constant(x, dtype=tf.float32))
model = MixtureGaussian(K=2, D=2)
variational = Variational()
variational.add(Dirichlet(1, model.K))
variational.add(Normal(model.K*model.D))
variational.add(InvGamma(model.K*model.D))
inference = ed.MFVI(model, variational, data)
inference.run(n_iter=10000, n_minibatch=5, n_data=5)
"""
Probability model
Posterior: (1-dimensional) Bernoulli
Variational model
Likelihood: Mean-field Bernoulli
"""
import edward as ed
import tensorflow as tf
from edward.stats import bernoulli
from edward.variationals import Variational, Bernoulli
class BernoulliPosterior:
"""
p(x, z) = p(z) = p(z | x) = Bernoulli(z; p)
"""
def __init__(self, p):
self.p = p
def log_prob(self, xs, zs):
return bernoulli.logpmf(zs, p)
ed.set_seed(42)
p = tf.constant(0.6)
model = BernoulliPosterior(p)
variational = Variational()
variational.add(Bernoulli(1))
inference = ed.MFVI(model, variational)
inference.run(n_iter=10000)
"""
import edward as ed
import tensorflow as tf
from edward.stats import bernoulli, beta
from edward.variationals import Variational, Beta
class BetaBernoulli:
"""
p(x, z) = Bernoulli(x | z) * Beta(z | 1, 1)
"""
def __init__(self):
self.num_vars = 1
def log_prob(self, xs, zs):
log_prior = beta.logpdf(zs, a=1.0, b=1.0)
log_lik = tf.pack([tf.reduce_sum(bernoulli.logpmf(xs, z)) \
for z in tf.unpack(zs)])
return log_lik + log_prior
ed.set_seed(42)
model = BetaBernoulli()
variational = Variational()
variational.add(Beta(model.num_vars))
data = ed.Data(tf.constant((0, 1, 0, 0, 0, 0, 0, 0, 0, 1), dtype=tf.float32))
inference = ed.MFVI(model, variational, data)
inference.run(n_iter=10000)
Variational model
Likelihood: Mean-field Beta
"""
import edward as ed
import tensorflow as tf
from edward.stats import bernoulli, beta
from edward.variationals import Variational, Beta
class BetaBernoulli:
"""
p(x, z) = Bernoulli(x | z) * Beta(z | 1, 1)
"""
def __init__(self):
self.num_vars = 1
def log_prob(self, xs, zs):
log_prior = beta.logpdf(zs, a=1.0, b=1.0)
log_lik = tf.pack([tf.reduce_sum(bernoulli.logpmf(xs, z)) \
for z in tf.unpack(zs)])
return log_lik + log_prior
ed.set_seed(42)
model = BetaBernoulli()
variational = Variational()
variational.add(Beta(model.num_vars))
data = ed.Data(tf.constant((0, 1, 0, 0, 0, 0, 0, 0, 0, 1), dtype=tf.float32))
inference = ed.MFVI(model, variational, data)
inference.run(n_iter=10000)
log_prior += invgamma.logpdf(sigmas[k * self.D], self.a,
self.b)
log_prior += invgamma.logpdf(sigmas[k * self.D + 1], self.a,
self.b)
log_lik = tf.constant(0.0, dtype=tf.float32)
for x in tf.unpack(xs):
for k in xrange(self.K):
log_lik += tf.log(pi[k])
log_lik += multivariate_normal.logpdf(
x, mus[(k * self.D):((k + 1) * self.D)],
sigmas[(k * self.D):((k + 1) * self.D)])
log_prob += [log_prior + log_lik]
return tf.pack(log_prob)
ed.set_seed(42)
x = np.loadtxt('data/mixture_data.txt', dtype='float32', delimiter=',')
data = ed.Data(tf.constant(x, dtype=tf.float32))
model = MixtureGaussian(K=2, D=2)
variational = Variational()
variational.add(Dirichlet(1, model.K))
variational.add(Normal(model.K * model.D))
variational.add(InvGamma(model.K * model.D))
inference = ed.MFVI(model, variational, data)
inference.run(n_iter=10000, n_minibatch=5, n_data=5)
class BernoulliPosterior:
"""
p(x, z) = p(z) = p(z | x) = Bernoulli(z; p)
"""
def __init__(self, p):
self.lp = tf.log(p)
self.num_vars = get_dims(p)[0]
def log_prob(self, xs, zs):
return tf.pack([self.table_lookup(z) for z in tf.unpack(zs)])
def table_lookup(self, x):
"""Look up value from the probability table."""
elem = self.lp
for d in range(self.num_vars):
elem = tf.gather(elem, tf.to_int32(x[d]))
return elem
ed.set_seed(42)
p = tf.constant(
[[0.4, 0.1],
[0.1, 0.4]])
model = BernoulliPosterior(p)
variational = Variational()
variational.add(Bernoulli(model.num_vars))
inference = ed.MFVI(model, variational)
inference.run()
