Information Technology Reference
In-Depth Information
T
ʳ
ˉ(
s
i
,
t
)
=
ʳ
c
,
b
·
1
(
s
i
=
c
)
·
1
(
t
=
b
)
·
ˀ(
c
,
b
)
(3.5)
c
∈
S
b
∈
T
where
ˀ(
c
,
b
)
is the edge weight of target attribute
b
and auxiliary attribute
c
in the
graph
G
,
ʳ(
c
,
b
)
is the attribute relation compatibility
ʨ(
s
i
,
t
)
between
s
i
and
t
.
T
: This poten-
tial is used to describe the dependency relations between auxiliary attributes
s
i
and
s
k
, which is parameterized as:
Auxiliary Attribute Versus Auxiliary Attribute Potential
ʷ
ˈ(
s
i
,
s
k
,
t
)
T
ʷ
ˈ(
s
i
,
s
k
,
t
)
=
ˈ
b
,
c
,
d
·
1
(
t
=
b
)
·
1
(
s
i
=
c
)
(3.6)
b
∈
T
c
∈
S
d
∈
S
·
1
(
s
k
=
d
)
·
ˀ(
c
,
d
)
where
ˀ(
c
,
d
)
is the edge weight of auxiliary attribute
c
and auxiliary attribute
d
in the graph
G
. The parameter
ˈ
b
,
c
,
d
measures the attribute relation compatibility
ʨ(
s
i
,
s
k
,
t
)
between auxiliary attribute labels
(
s
i
,
s
k
)
and target attribute label
t
.
3.4.3.2 Model Learning and Inference
We describe how to learn the model parameters from training data as well as how to
infer the attribute label based on these parameters.
Given
N
training examples of users
x
n
s
n
t
n
N
n
,
we aim to learn the model parameters
w
that produce the correct target attribute
label
t
. Note that the auxiliary attributes of the training samples are treated as latent
variables and automatically inferred in the model learning process. The information
of training samples of auxiliary attributes can be well exploited in designing potential
functions.
We adopt the structural latent SVM formulation [
12
,
36
] to learn the model as
follows:
U
={
(
,
,
)
}
1
(
n
=
1
,
2
,...,
N
)
=
N
1
2
2
min
w
w
+
C
1
1
ʾ
n
,ʾ
≥
0
n
=
x
(
n
)
,
t
(
n
)
)
−
x
(
n
)
,
w
T
w
T
s.t. max
s
ʦ(
s
,
max
s
ʦ(
s
,
t
)
(3.7)
t
(
n
)
)
−
ʾ
n
,
∀
≥
ʔ(
t
,
n
,
∀
t
∈
T
where
C
1
is the trade-off parameter similar to that in SVMs, and
ʾ
n
is the slack vari-
able for the
n
th training example to handle soft-margin. Such an objective function
requires that the score for ground-truth target attribute label
t
(
n
)
is much higher than
those for other labels. The difference is recorded in a 0-1 loss function
t
(
n
)
)
ʔ(
t
,
:
