(c)
Suppose
two-thirds
of
the
data
belong
to
the
positive
class
and
the
remaining
one-third
belong
to
the
negative
class.
What
is
the
expected
error
of
a
classifier
that
predicts
every
test
record
to
be
positive?
Answer:
33.33%
There
are
66.66%
"+"
and
33.33%
"-"
classes.
The
classifier
predicts
every
test
record
to
be
"+".
The
Confusion
Matrix
for
above
classification
problem
Actual
"+"
Actual
"-*
Predicted
"+"
TP
=
66.66%
FP
=33.33%
Predicted
"-°
FN=0
TN=0
The
expected
error
=
(FP
+
FN)
/
(TP
+
FP
+
FN
+
TN)
=
33.33%/100%
=
33.33%
(d)
Repeat
the
previous
analysis
assuming
that
the
classifier
predicts
each
test
record
to
be
positive
class
with
probability
2/3
and
negative
class
with
probability
1/3.
Answer:
44.44%.
There
are
66.66%
"+"
and
33.33%
"-"
classes.
The
classifier
predicts
"+"
with
probability
2/3.
TP
=
66.66%o0f
"+"
data
*
2/3
=
44
.44%
and
Hence
FN
=
22.22%
The
classifier
predicts
"-"
with
probability
1/3
TN
=
33.33%
of
"-"
data
*
1/3
=
11.11%
and
hence
FP
=
22.22%
The
Confusion
Matrix
for
above
classification
problem
Actual
"+"
Actual
*-*
Predicted
"+"
TP
=
44
.44%
FP
=22.22%
Predicted
"-"
FN
=
22.22%
TN
=
33.33%
The
expected
error=(FP
+
FN)/
(TP
+
FP
+
FN
+
TN)
=
44.44%/100%
=
44.44%