# we like to calculate posterior p(\theta|x) where \theta=[mu_1,..., mu_3, sigma_1,...,sigma_3, z_1,...,z_3]
# Model
pi = Dirichlet(np.ones(K, np.float32))
mu = Normal(0.0, 9.0, sample_shape=[K])
sigma = InverseGamma(1.0, 1.0, sample_shape=[K])
c = Categorical(logits=tf.log(pi) - tf.log(1.0 - pi), sample_shape=N)
ed_x = Normal(loc=tf.gather(mu, c), scale=tf.gather(sigma, c))
# parameters
q_pi = Dirichlet(
tf.nn.softplus(
tf.get_variable("qpi", [K],
initializer=tf.constant_initializer(1.0 / K))))
q_mu = Normal(loc=tf.get_variable("qmu", [K]), scale=1.0)
q_sigma = Normal(loc=tf.nn.softplus(tf.get_variable("qsigma", [K])), scale=1.0)
inference = ed.KLqp(latent_vars={
mu: q_mu,
sigma: q_sigma
}, data={ed_x: x}) # this will fail if we include qpi: pi
inference.run(n_iter=1000)
print q_pi.value().eval()
print q_mu.value().eval()
print q_sigma.value().eval()
We build a random variable whose size depends on a sample from another random variable. """ from __future__ import absolute_import from __future__ import division from __future__ import print_function import edward as ed import tensorflow as tf from edward.models import Exponential, Dirichlet, Gamma ed.set_seed(42) # Prior on scalar hyperparameter to Dirichlet. alpha = Gamma(alpha=1.0, beta=1.0) # Prior on size of Dirichlet. n = 1 + tf.cast(Exponential(lam=0.5), tf.int32) # Build a vector of ones whose size is n; multiply it by alpha. p = Dirichlet(alpha=tf.ones([n]) * alpha) sess = ed.get_session() print(sess.run(p.value())) # [ 0.01012419 0.02939712 0.05036638 0.51287931 0.31020424 0.0485355 # 0.0384932 ] print(sess.run(p.value())) # [ 0.12836078 0.23335715 0.63828212]
