Database Reference
In-Depth Information
Classification rule
A
,
B
→
C
benefit (
C
)
group denied granted
protected (
A
)
a
b
n
1
unprotected (
¬
A
)
c
d
n
2
m
1
m
2
n
(total of
B
)
p
1
=
a
/
n
1
p
2
=
c
/
n
2
p
=
m
1
/
n
p
1
p
2
1
−
p
1
1
−
p
2
RR
RC
=
a
/
b
c
/
d
RD
=
p
1
−
p
2
RR
=
RC
=
OR
=
p
1
p
1
p
1
1
−
p
−
ED
=
p
1
−
pER
=
EC
=
Fig. 5.1
Contingency table and discrimination measures
Definition 3.
Let
A
,
B
→
C
be a PD classification rule with
con f
(
B
→
C
)
>
0. The
extended lift of the rule is:
(
,
→
)
con f
A
B
C
elift
(
A
,
B
→
C
)=
.
con f
(
B
→
C
)
Arule
SEX
=
FEMALE
,
CAR
=
OWN
CREDIT
=
NO
with an extended lift of 3 means
that being a female increases 3 times the probability of being refused credit with
respect to the average confidence of people owning a car. While this means that
women are discriminated among car owners, notice that we cannot conclude that
being a woman is the actual reason of discrimination (see Sect. 5.5 for a discussion).
An alternative way, yet equivalent, of defining the extend lift is as the ratio between
the proportion of the disadvantaged group
A
in context
B
obtaining the benefit
C
over the overall proportion of
A
in
B
:
→
(
,
→
)
con f
B
C
A
.
con f
(
B
→
A
)
This makes it clear how extended lift relates to the principle of group over-represen-
tation in benefit denying, or, equivalently, of group under-representation in benefit
granting. In addition to extended lift, other measures can be formalized starting
from different definitions of discrimination provided by laws. They can be defined
over the 2
2 contingency table shown in Figure 5.1, showing the absolute num-
ber of transactions in the underlying dataset
×
satisfying the itemsets in the X-Y
coordinates and the context
B
.Let
p
1
(resp.,
p
2
) be the proportion of people in the
protected group (resp., not in the protected group) that were not granted a bene-
fit, and let
p
be the proportion of all people (both protected and not) that were not
granted the benefit. The following discrimination measures can be defined:
D
•
risk difference
(RD
=
p
1
−
p
2
), also known as
absolute risk reduction
,
•
risk ratio
or
relative risk
(RR
=
p
1
/
p
2
),
Search WWH ::
Custom Search