Implementation of Hamiltonian Monte Carlo using Google's TensorFlow
In gaussian_sampler_example.py there is an example of sampling from either a diagonal, 0-mean Gaussian distribution or a correlated Gaussian distribution.
To use HMC, you need to define a log-posterior function (unnormalized)
Example: mean=0, correlation=0.8 Gaussian
def gaussian_log_posterior_correlated(x):
covariance = tf.constant(
np.array([
[1.0, 0.8],
[0.8, 1.0]]),
dtype=tf.float32
)
covariance_inverse = tf.matrix_inverse(covariance)
xA = tf.matmul(x, covariance_inverse)
xAx = tf.matmul(xA, tf.transpose(x))
return xAx / 2.0from hamiltonian_monte_carlo import hmc
num_samples = 20
# Number of dimensions for samples
ndim = 2
session = tf.Session()
with session.as_default():
print("Drawing from a correlated Gaussian...")
initial_x = tf.Variable(
tf.random_normal(
(1, ndim),
dtype=tf.float32)
)
session.run(tf.initialize_all_variables())
for i in xrange(num_samples):
sample = session.run(
hmc(initial_x,
log_posterior=gaussian_log_posterior_correlated,
step_size=0.1,
num_steps=10)
)
print(sample)