<s>
The	O
mean	B-General_Concept
absolute	I-General_Concept
percentage	I-General_Concept
error	I-General_Concept
(	O
MAPE	B-General_Concept
)	O
,	O
also	O
known	O
as	O
mean	O
absolute	O
percentage	O
deviation	O
(	O
MAPD	B-General_Concept
)	O
,	O
is	O
a	O
measure	O
of	O
prediction	O
accuracy	O
of	O
a	O
forecasting	O
method	O
in	O
statistics	O
.	O
</s>
<s>
Mean	B-General_Concept
absolute	I-General_Concept
percentage	I-General_Concept
error	I-General_Concept
is	O
commonly	O
used	O
as	O
a	O
loss	O
function	O
for	O
regression	O
problems	O
and	O
in	O
model	O
evaluation	O
,	O
because	O
of	O
its	O
very	O
intuitive	O
interpretation	O
in	O
terms	O
of	O
relative	O
error	O
.	O
</s>
<s>
In	O
the	O
classical	O
regression	O
setting	O
,	O
the	O
closeness	O
of	O
to	O
is	O
measured	O
via	O
the	O
risk	O
,	O
also	O
called	O
the	O
mean	B-Algorithm
squared	I-Algorithm
error	I-Algorithm
(	O
MSE	O
)	O
.	O
</s>
<s>
In	O
the	O
MAPE	B-General_Concept
regression	O
context	O
,	O
the	O
closeness	O
of	O
to	O
is	O
measured	O
via	O
the	O
MAPE	B-General_Concept
,	O
and	O
the	O
aim	O
of	O
MAPE	B-General_Concept
regressions	O
is	O
to	O
find	O
a	O
model	O
such	O
that	O
:	O
</s>
<s>
From	O
a	O
practical	O
point	O
of	O
view	O
,	O
the	O
use	O
of	O
the	O
MAPE	B-General_Concept
as	O
a	O
quality	O
function	O
for	O
regression	O
model	O
is	O
equivalent	O
to	O
doing	O
weighted	O
mean	B-General_Concept
absolute	I-General_Concept
error	I-General_Concept
(	O
MAE	O
)	O
regression	O
,	O
also	O
known	O
as	O
quantile	O
regression	O
.	O
</s>
<s>
As	O
a	O
consequence	O
,	O
the	O
use	O
of	O
the	O
MAPE	B-General_Concept
is	O
very	O
easy	O
in	O
practice	O
,	O
for	O
example	O
using	O
existing	O
libraries	O
for	O
quantile	O
regression	O
allowing	O
weights	O
.	O
</s>
<s>
The	O
use	O
of	O
the	O
MAPE	B-General_Concept
as	O
a	O
loss	O
function	O
for	O
regression	O
analysis	O
is	O
feasible	O
both	O
on	O
a	O
practical	O
point	O
of	O
view	O
and	O
on	O
a	O
theoretical	O
one	O
,	O
since	O
the	O
existence	O
of	O
an	O
optimal	O
model	O
and	O
the	O
consistency	O
of	O
the	O
empirical	B-General_Concept
risk	I-General_Concept
minimization	I-General_Concept
can	O
be	O
proved	O
.	O
</s>
<s>
WMAPE	O
(	O
sometimes	O
spelled	O
wMAPE	O
)	O
stands	O
for	O
weighted	B-General_Concept
mean	I-General_Concept
absolute	I-General_Concept
percentage	I-General_Concept
error	I-General_Concept
.	O
</s>
<s>
It	O
is	O
a	O
variant	O
of	O
MAPE	B-General_Concept
in	O
which	O
the	O
mean	O
absolute	O
percent	O
errors	O
is	O
treated	O
as	O
a	O
weighted	O
arithmetic	O
mean	O
.	O
</s>
<s>
Perhaps	O
it	O
would	O
be	O
more	O
accurate	O
to	O
call	O
this	O
the	O
double	O
weighted	O
MAPE	B-General_Concept
(	O
wwMAPE	O
)	O
.	O
</s>
<s>
Although	O
the	O
concept	O
of	O
MAPE	B-General_Concept
sounds	O
very	O
simple	O
and	O
convincing	O
,	O
it	O
has	O
major	O
drawbacks	O
in	O
practical	O
application	O
,	O
and	O
there	O
are	O
many	O
studies	O
on	O
shortcomings	O
and	O
misleading	O
results	O
from	O
MAPE	B-General_Concept
.	O
</s>
<s>
It	O
cannot	O
be	O
used	O
if	O
there	O
are	O
zero	O
or	O
close-to-zero	O
values	O
(	O
which	O
sometimes	O
happens	O
,	O
for	O
example	O
in	O
demand	O
data	O
)	O
because	O
there	O
would	O
be	O
a	O
division	O
by	O
zero	O
or	O
values	O
of	O
MAPE	B-General_Concept
tending	O
to	O
infinity	O
.	O
</s>
<s>
MAPE	B-General_Concept
puts	O
a	O
heavier	O
penalty	O
on	O
negative	O
errors	O
,	O
than	O
on	O
positive	O
errors	O
.	O
</s>
<s>
As	O
a	O
consequence	O
,	O
when	O
MAPE	B-General_Concept
is	O
used	O
to	O
compare	O
the	O
accuracy	O
of	O
prediction	O
methods	O
it	O
is	O
biased	O
in	O
that	O
it	O
will	O
systematically	O
select	O
a	O
method	O
whose	O
forecasts	O
are	O
too	O
low	O
.	O
</s>
<s>
People	O
often	O
think	O
the	O
MAPE	B-General_Concept
will	O
be	O
optimized	O
at	O
the	O
median	O
.	O
</s>
<s>
But	O
for	O
example	O
,	O
a	O
log	O
normal	O
has	O
a	O
median	O
of	O
where	O
as	O
it	O
is	O
MAPE	B-General_Concept
optimized	O
at	O
.	O
</s>
<s>
To	O
overcome	O
these	O
issues	O
with	O
MAPE	B-General_Concept
,	O
there	O
are	O
some	O
other	O
measures	O
proposed	O
in	O
literature	O
:	O
</s>
<s>
Mean	O
Arctangent	O
Absolute	O
Percentage	O
Error	O
(	O
MAAPE	O
)	O
:	O
MAAPE	O
can	O
be	O
considered	O
a	O
slope	O
as	O
an	O
angle	O
,	O
while	O
MAPE	B-General_Concept
is	O
a	O
slope	O
as	O
a	O
ratio	O
.	O
</s>
