D = 3 # dimension
cov = [[ 1.36, 0.62, 0.93],
[ 0.80, 1.19, 0.43],
[ 0.57, 0.73, 1.06]]
# model
z = MultivariateNormalTriL(loc=tf.ones(D),
scale_tril=tf.cholesky(cov))
# inference
qz = MultivariateNormalTriL(loc=tf.Variable(tf.zeros(D)),
scale_tril=tf.nn.softplus(tf.Variable(tf.zeros((D, D)))))
inference = ed.KLqp({z:qz})
# qz = Empirical(tf.Variable(tf.random_normal([T,D])))
# inference = ed.HMC({z:qz})
inference.run()
# criticism
sess = ed.get_session()
mean, stddev = sess.run([qz.mean(), qz.stddev()])
print("Inferred posterior mean: ", mean)
print("Inferred post erior stddev: ", stddev)
a = sess.run(qz.sample(5000))
# plot
fig = plt.figure()
ax = Axes3D(fig)
ax.plot(a[:, 0], a[:, 1], a[:, 2], "o")
plt.show()
m_prior = tf.constant(np.array([0.5, 0.5]), dtype=tf.float64)
k_prior = tf.constant(0.6, dtype=tf.float64)
# Posterior inference
# Probabilistic model
sigma = WishartCholesky(df=v_prior, scale=W_prior)
mu = MultivariateNormalTriL(m_prior, k_prior * sigma)
xn = MultivariateNormalTriL(tf.reshape(tf.tile(mu, [N]), [N, D]),
tf.reshape(tf.tile(sigma, [N, 1]), [N, 2, 2]))
# Variational model
# Variational model
qmu = MultivariateNormalTriL(
tf.Variable(tf.random_normal([D], dtype=tf.float64)),
tf.nn.softplus(tf.Variable(tf.random_normal([D, D], dtype=tf.float64))))
L = tf.Variable(tf.random_normal([D, D], dtype=tf.float64))
qsigma = WishartCholesky(
tf.nn.softplus(
tf.Variable(tf.random_normal([], dtype=tf.float64)) + D + 1),
LinearOperatorTriL(L).to_dense())
# Inference
inference = ed.KLqp({mu: qmu, sigma: qsigma}, data={xn: xn_data})
inference.run(n_iter=N_ITERS, n_samples=N_SAMPLES)
sess = ed.get_session()
print('Inferred mu: {}'.format(sess.run(qmu.mean())))
print('Inferred precision: {}'.format(sess.run(qsigma.mean())))
print('Inferred sigma: {}'.format(sess.run(1 / qsigma.mean())))
