X1
X2
.
Xn
Y1
Y2
.
Yn
Z1
Z2
.
Zn
Figure 1: The sigmoid network
2
BP in Sigmoid Networks
Solution due to Steve Gardiner
1. Write down the belief propagation updates for the network.
Figure 2 shows the
D) its reserves must equal 50% of its money supply.
54. If domestic credit is constant, then any change in the demand for money will result in:
A) a change in foreign credit.
B) a change in the rate o
P
k)
= n nk xn . Next, we maximize each clusters regression coefficient vector k . We can
because J(
k
analytically solve for k by setting its derivative to zero.
k)
J(
k
=
X
nk
n
0 =
X
cfw_(yn kT
HMM result See Figure 1a for log-likelihood. The log-likelihood score on the test data (2.5517 103)
was approximately similar to that of the train data (2.4726 103 ). The results of HMM training and
t
3.2
Marginals
By Bayes rule,
P (cfw_xi ) =
by Eq.2, 3
by Eq.4
P (cfw_hj , xi )
P (cfw_hj |cfw_xi )
X
X
X
X
jb
ia fia (xi ) +
jb gjb (hj ) +
Wia
fia (xi )gjb (hj )
jb gjb (hj )
exp
i,a
j,b
i,j,a,b
j