Dear users,
I try to deal with a simple model which has not only observations, but observations and its uncertainties. I’ve modified the normal_normal example at Github in order to include uncertainties. I’ve also included KLqp instead of HMC. Is this the correct way to do this? The problem I see in my code is the following:
x_obs = Normal(loc=x, scale = x_s)
because the shape grows as N
does, which affects to KLqp. For instance if N=100000
then
`>>> x_obs.shape
TensorShape([Dimension(100000)])
Maybe it’s better to split the dataset as @dustin does at Data Subsampling section? What do you think?
The modified normal_normal.py example:
"""Normal-normal model using Hamiltonian Monte Carlo."""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
import edward as ed
import matplotlib.pyplot as plt
import numpy as np
import tensorflow as tf
from edward.models import Empirical, Normal
def main(_):
ed.set_seed(42)
# DATA
N=100000
x_data = np.array([0.0] * N)
x_uncert = np.random.normal(size=N)
# MODEL: Normal-Normal with known variance
mu = Normal(loc=0.0, scale=1.0)
x = Normal(loc=mu, scale=1.0)
x_s = tf.placeholder(tf.float32, [N])
x_obs = Normal(loc=x, scale = x_s)
# INFERENCE
qmu = Normal(loc=tf.Variable(tf.random_normal([])), scale=tf.nn.softplus(tf.Variable(tf.random_normal([]))))
# analytic solution: N(loc=0.0, scale=\sqrt{1/51}=0.140)
inference = ed.KLqp({mu: qmu}, data={x_obs: x_data, x_s: x_uncert})
inference.run()
# CRITICISM
sess = ed.get_session()
mean, stddev = sess.run([qmu.mean(), qmu.stddev()])
print("Inferred posterior mean:")
print(mean)
print("Inferred posterior stddev:")
print(stddev)
# Check convergence with visual diagnostics.
samples = sess.run(qmu.sample(1000))
# Plot histogram.
plt.hist(samples, bins='auto')
plt.show()
# Trace plot.
plt.plot(samples)
plt.show()
if __name__ == "__main__":
tf.app.run()