April 2016
Beginner to intermediate
463 pages
18h 53m
English
Content preview from Big Data
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Big Data and Information Distillation
131
To get θ
∗
that maximizes Q
θ|θ
(t)
, the derivatives are set to 0:
∂
Q
∂
a
i
= 0,
∂
Q
∂
b
i
= 0,
∂
Q
∂
d
= 0
which yields
N
∑
j=1
Z(t, j)
S
i
C
j
1
a
∗
i
−(1 −S
i
C
j
)
1
1 −a
∗
i
= 0
N
∑
j=1
(1 −Z(t, j))
S
i
C
j
1
b
∗
i
−(1 −S
i
C
j
)
1
1 −b
∗
i
= 0
N
∑
j=1
Z(t, j)M
1
d
∗
−
(1 −Z(t, j))M
1
1 −d
∗
= 0 (5.16)
Let us define SJ
i
as the set of claims the source S
i
actually observes in the observation matrix
SC, and
SJ
i
as the set of claims source S
i
does not observe. Thus, Equation 5.16 can be
rewritten as
∑
j∈SJ
i
Z(t, j)
1
a
∗
i
−
∑
j∈SJ
i
Z(t, j)
1
1 −a
∗
i
= 0
∑
j∈SJ
i
(1 −Z(t, j))
1
b
∗
i
−
∑
j∈SJ
i
(1 −Z(t, j))
1
1 −b
∗
i
= 0
N
∑
j=1
Z(t, j)
1
d
∗
−
(1 −Z(t, j))
1
1 −d
∗
= 0 (5.17)
Solving the above equations, the