Modify Bayesian Linear Model to use Gibbs, but got NotImplementedError

1

Just start to learn Edward.
I tried the Bayesian Linear Model example. Then, I tried to do a little venture. I want to assume a conjugate prior for the covariance of y. Then, use Gibbs sampling to estimate it.

%matplotlib inline
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 Normal, Empirical

plt.style.use('ggplot')

def build_toy_dataset(N, w):
  D = len(w)
  x = np.random.normal(0.0, 2.0, size=(N, D))
  y = np.dot(x, w) + np.random.normal(0.0, 0.01, size=N)
  return x, y


ed.set_seed(42)

N = 40  # number of data points
D = 10  # number of features

w_true = np.random.randn(D) * 0.5
X_train, y_train = build_toy_dataset(N, w_true)
X_test, y_test = build_toy_dataset(N, w_true)

from edward.models import InverseGamma, Gamma

X = tf.placeholder(tf.float32, [N, D])
w = Normal(loc=tf.zeros(D), scale=tf.ones(D))
b = Normal(loc=tf.zeros(1), scale=tf.ones(1))
sigma_y = InverseGamma(tf.ones(N), tf.ones(N), sample_shape=1)
y = Normal(loc=ed.dot(X, w) + b, scale=sigma_y)

T = 500  # number of MCMC samples
qsigma_y = Empirical(tf.get_variable(
    "qsigma_y/params", [T, 1, N],
    initializer=tf.ones_initializer()))

inference = ed.Gibbs({sigma_y: qsigma_y}, data={X: X_train, y: y_train})
inference.run(n_sample=1, n_iter=250)

Then, I got the error:

---------------------------------------------------------------------------
NotImplementedError                       Traceback (most recent call last)
<ipython-input-8-b6599950810a> in <module>()
----> 1 inference = ed.Gibbs({sigma_y: qsigma_y}, data={X: X_train, y: y_train})
      2 inference.run(n_sample=1, n_iter=250)

~/.virtualenvs/tensorflow-gpu/lib/python3.6/site-packages/edward/inferences/gibbs.py in __init__(self, latent_vars, proposal_vars, data)
     44     if proposal_vars is None:
     45       proposal_vars = {z: complete_conditional(z)
---> 46                        for z in six.iterkeys(latent_vars)}
     47     else:
     48       check_latent_vars(proposal_vars)

~/.virtualenvs/tensorflow-gpu/lib/python3.6/site-packages/edward/inferences/gibbs.py in <dictcomp>(.0)
     44     if proposal_vars is None:
     45       proposal_vars = {z: complete_conditional(z)
---> 46                        for z in six.iterkeys(latent_vars)}
     47     else:
     48       check_latent_vars(proposal_vars)

~/.virtualenvs/tensorflow-gpu/lib/python3.6/site-packages/edward/inferences/conjugacy/conjugacy.py in complete_conditional(rv, cond_set)
    128                                 'statistics %s, but no available '
    129                                 'exponential-family distribution has those '
--> 130                                 'sufficient statistics.' % str(dist_key))
    131 
    132     # Swap sufficient statistics for placeholders, then take gradients

NotImplementedError: Conditional distribution has sufficient statistics (('#CPow-1.0000e+00', ('#x',)), ('#CPow-2.0000e+00', ('#x',)), ('#Log', ('#x',))), but no available exponential-family distribution has those sufficient statistics.

What is the problem? and, what should I change to make it work?

Thank you!