def collapsed_sample_f(self, theta,n,A,f):
"""
Use a collapsed Gibbs sampler to update the block assignments
by integrating out the block-to-block connection probabilities B.
Since this is a Beta-Bernoulli model the posterior can be computed
in closed form and the integral can be computed analytically.
"""
(B,pi) = theta
A = A.astype(np.bool)
zother = np.array(f).astype(np.int)
# P(A|z) \propto
# \prod_{r1}\prod_{r2} Beta(m(r1,r2)+b1,\hat{m}(r1,r2)+b0) /
# Beta(b1,b0)
#
# Switching z changes the product over r1 and the product over r2
# Compute the posterior distribution over blocks
# TODO: This literal translation of the log prob is O(R^3)
# But it can almost certainly be sped up to O(R^2)
ln_pi_post = np.log(pi)
for r in np.arange(self.R):
zother[n] = r
for r1 in np.arange(self.R):
for r2 in np.arange(self.R):
# Look at outgoing edges under z[n] = r
Ar1r2 = A[np.ix_(zother==r1,zother==r2)]
mr1r2 = np.sum(Ar1r2)
hat_mr1r2 = Ar1r2.size - mr1r2
ln_pi_post[r] += betaln(mr1r2+self.b1, hat_mr1r2+self.b0) - \
betaln(self.b1,self.b0)
zn = log_sum_exp_sample(ln_pi_post)
return zn
def naive_sample_f(self, theta, n, A, f, beta=1.0):
"""
Naively Gibbs sample z given B and pi
"""
(B,pi) = theta
A = A.astype(np.bool)
zother = np.array(f).astype(np.int)
# Compute the posterior distribution over blocks
ln_pi_post = np.log(pi)
rrange = np.arange(self.R)
for r in rrange:
zother[n] = r
# Block IDs of nodes we connect to
o1 = A[n,:]
if np.any(A[n,:]):
ln_pi_post[r] += beta * np.sum(np.log(B[np.ix_([r],zother[o1])]))
# Block IDs of nodes we don't connect to
o2 = np.logical_not(A[n,:])
if np.any(o2):
ln_pi_post[r] += beta * np.sum(np.log(1-B[np.ix_([r],zother[o2])]))
# Block IDs of nodes that connect to us
i1 = A[:,n]
if np.any(i1):
ln_pi_post[r] += beta * np.sum(np.log(B[np.ix_(zother[i1],[r])]))
# Block IDs of nodes that do not connect to us
i2 = np.logical_not(A[:,n])
if np.any(i2):
ln_pi_post[r] += beta * np.sum(np.log(1-B[np.ix_(zother[i2],[r])]))
zn = log_sum_exp_sample(ln_pi_post)
return zn
