<s>
In	O
statistics	O
,	O
imputation	B-General_Concept
is	O
the	O
process	O
of	O
replacing	O
missing	O
data	O
with	O
substituted	O
values	O
.	O
</s>
<s>
When	O
substituting	O
for	O
a	O
data	O
point	O
,	O
it	O
is	O
known	O
as	O
"	O
unit	O
imputation	B-General_Concept
"	O
;	O
when	O
substituting	O
for	O
a	O
component	O
of	O
a	O
data	O
point	O
,	O
it	O
is	O
known	O
as	O
"	O
item	O
imputation	B-General_Concept
"	O
.	O
</s>
<s>
Because	O
missing	O
data	O
can	O
create	O
problems	O
for	O
analyzing	O
data	O
,	O
imputation	B-General_Concept
is	O
seen	O
as	O
a	O
way	O
to	O
avoid	O
pitfalls	O
involved	O
with	O
listwise	O
deletion	O
of	O
cases	O
that	O
have	O
missing	O
values	O
.	O
</s>
<s>
That	O
is	O
to	O
say	O
,	O
when	O
one	O
or	O
more	O
values	O
are	O
missing	O
for	O
a	O
case	O
,	O
most	O
statistical	B-Algorithm
packages	I-Algorithm
default	O
to	O
discarding	O
any	O
case	O
that	O
has	O
a	O
missing	O
value	O
,	O
which	O
may	O
introduce	O
bias	O
or	O
affect	O
the	O
representativeness	O
of	O
the	O
results	O
.	O
</s>
<s>
Imputation	B-General_Concept
preserves	O
all	O
cases	O
by	O
replacing	O
missing	O
data	O
with	O
an	O
estimated	O
value	O
based	O
on	O
other	O
available	O
information	O
.	O
</s>
<s>
A	O
few	O
of	O
the	O
well	O
known	O
attempts	O
to	O
deal	O
with	O
missing	O
data	O
include	O
:	O
hot	O
deck	O
and	O
cold	O
deck	O
imputation	B-General_Concept
;	O
listwise	O
and	O
pairwise	O
deletion	O
;	O
mean	O
imputation	B-General_Concept
;	O
non-negative	O
matrix	O
factorization	O
;	O
regression	O
imputation	B-General_Concept
;	O
last	O
observation	O
carried	O
forward	O
;	O
stochastic	O
imputation	B-General_Concept
;	O
and	O
multiple	B-General_Concept
imputation	I-General_Concept
.	O
</s>
<s>
If	O
the	O
data	O
are	O
missing	O
completely	O
at	O
random	O
,	O
then	O
listwise	O
deletion	O
does	O
not	O
add	O
any	O
bias	O
,	O
but	O
it	O
does	O
decrease	O
the	O
power	B-General_Concept
of	O
the	O
analysis	O
by	O
decreasing	O
the	O
effective	O
sample	O
size	O
.	O
</s>
<s>
A	O
once-common	O
method	O
of	O
imputation	B-General_Concept
was	O
hot-deck	O
imputation	B-General_Concept
where	O
a	O
missing	O
value	O
was	O
imputed	O
from	O
a	O
randomly	O
selected	O
similar	O
record	O
.	O
</s>
<s>
The	O
term	O
"	O
hot	O
deck	O
"	O
dates	O
back	O
to	O
the	O
storage	O
of	O
data	O
on	O
punched	B-Architecture
cards	I-Architecture
,	O
and	O
indicates	O
that	O
the	O
information	O
donors	O
come	O
from	O
the	O
same	O
dataset	O
as	O
the	O
recipients	O
.	O
</s>
<s>
One	O
form	O
of	O
hot-deck	O
imputation	B-General_Concept
is	O
called	O
"	O
last	O
observation	O
carried	O
forward	O
"	O
(	O
or	O
LOCF	O
for	O
short	O
)	O
,	O
which	O
involves	O
sorting	O
a	O
dataset	O
according	O
to	O
any	O
of	O
a	O
number	O
of	O
variables	O
,	O
thus	O
creating	O
an	O
ordered	O
dataset	O
.	O
</s>
<s>
Cold-deck	O
imputation	B-General_Concept
,	O
by	O
contrast	O
,	O
selects	O
donors	O
from	O
another	O
dataset	O
.	O
</s>
<s>
Due	O
to	O
advances	O
in	O
computer	O
power	B-General_Concept
,	O
more	O
sophisticated	O
methods	O
of	O
imputation	B-General_Concept
have	O
generally	O
superseded	O
the	O
original	O
random	O
and	O
sorted	O
hot	O
deck	O
imputation	B-General_Concept
techniques	I-General_Concept
.	O
</s>
<s>
Another	O
imputation	B-General_Concept
technique	O
involves	O
replacing	O
any	O
missing	O
value	O
with	O
the	O
mean	O
of	O
that	O
variable	O
for	O
all	O
other	O
cases	O
,	O
which	O
has	O
the	O
benefit	O
of	O
not	O
changing	O
the	O
sample	O
mean	O
for	O
that	O
variable	O
.	O
</s>
<s>
However	O
,	O
mean	O
imputation	B-General_Concept
attenuates	O
any	O
correlations	O
involving	O
the	O
variable(s )	O
that	O
are	O
imputed	O
.	O
</s>
<s>
This	O
is	O
because	O
,	O
in	O
cases	O
with	O
imputation	B-General_Concept
,	O
there	O
is	O
guaranteed	O
to	O
be	O
no	O
relationship	O
between	O
the	O
imputed	O
variable	O
and	O
any	O
other	O
measured	O
variables	O
.	O
</s>
<s>
Thus	O
,	O
mean	O
imputation	B-General_Concept
has	O
some	O
attractive	O
properties	O
for	O
univariate	O
analysis	O
but	O
becomes	O
problematic	O
for	O
multivariate	O
analysis	O
.	O
</s>
<s>
Mean	O
imputation	B-General_Concept
can	O
be	O
carried	O
out	O
within	O
classes	O
(	O
i.e.	O
</s>
<s>
This	O
is	O
a	O
special	O
case	O
of	O
generalized	O
regression	O
imputation	B-General_Concept
:	O
</s>
<s>
This	O
makes	O
it	O
a	O
mathematically	O
proven	O
method	O
for	O
data	B-General_Concept
imputation	I-General_Concept
.	O
</s>
<s>
Regression	O
imputation	B-General_Concept
has	O
the	O
opposite	O
problem	O
of	O
mean	O
imputation	B-General_Concept
.	O
</s>
<s>
Stochastic	O
regression	O
was	O
a	O
fairly	O
successful	O
attempt	O
to	O
correct	O
the	O
lack	O
of	O
an	O
error	O
term	O
in	O
regression	O
imputation	B-General_Concept
by	O
adding	O
the	O
average	O
regression	O
variance	O
to	O
the	O
regression	O
imputations	B-General_Concept
to	O
introduce	O
error	O
.	O
</s>
<s>
In	O
order	O
to	O
deal	O
with	O
the	O
problem	O
of	O
increased	O
noise	O
due	O
to	O
imputation	B-General_Concept
,	O
Rubin	O
(	O
1987	O
)	O
developed	O
a	O
method	O
for	O
averaging	O
the	O
outcomes	O
across	O
multiple	O
imputed	O
data	O
sets	O
to	O
account	O
for	O
this	O
.	O
</s>
<s>
All	O
multiple	B-General_Concept
imputation	I-General_Concept
methods	O
follow	O
three	O
steps	O
.	O
</s>
<s>
Imputation	B-General_Concept
–	O
Similar	O
to	O
single	B-General_Concept
imputation	I-General_Concept
,	O
missing	O
values	O
are	O
imputed	O
.	O
</s>
<s>
Just	O
as	O
there	O
are	O
multiple	O
methods	O
of	O
single	B-General_Concept
imputation	I-General_Concept
,	O
there	O
are	O
multiple	O
methods	O
of	O
multiple	B-General_Concept
imputation	I-General_Concept
as	O
well	O
.	O
</s>
<s>
One	O
advantage	O
that	O
multiple	B-General_Concept
imputation	I-General_Concept
has	O
over	O
the	O
single	B-General_Concept
imputation	I-General_Concept
and	O
complete	O
case	O
methods	O
is	O
that	O
multiple	B-General_Concept
imputation	I-General_Concept
is	O
flexible	O
and	O
can	O
be	O
used	O
in	O
a	O
wide	O
variety	O
of	O
scenarios	O
.	O
</s>
<s>
Multiple	B-General_Concept
imputation	I-General_Concept
can	O
be	O
used	O
in	O
cases	O
where	O
the	O
data	O
are	O
missing	O
completely	O
at	O
random	O
,	O
missing	O
at	O
random	O
,	O
and	O
even	O
when	O
the	O
data	O
are	O
missing	O
not	O
at	O
random	O
.	O
</s>
<s>
A	O
popular	O
approach	O
is	O
multiple	B-General_Concept
imputation	I-General_Concept
by	O
chained	O
equations	O
(	O
MICE	O
)	O
,	O
also	O
known	O
as	O
"	O
fully	O
conditional	O
specification	O
"	O
and	O
"	O
sequential	O
regression	O
multiple	O
imputation.	O
"	O
</s>
<s>
More	O
recent	O
approaches	O
to	O
multiple	B-General_Concept
imputation	I-General_Concept
use	O
machine	O
learning	O
techniques	O
to	O
improve	O
its	O
performance	O
.	O
</s>
<s>
MIDAS	O
(	O
Multiple	B-General_Concept
Imputation	I-General_Concept
with	O
Denoising	O
Autoencoders	B-Algorithm
)	O
,	O
for	O
instance	O
,	O
uses	O
denoising	O
autoencoders	B-Algorithm
,	O
a	O
type	O
of	O
unsupervised	O
neural	O
network	O
,	O
to	O
learn	O
fine-grained	O
latent	O
representations	O
of	O
the	O
observed	O
data	O
.	O
</s>
<s>
MIDAS	O
has	O
been	O
shown	O
to	O
provide	O
accuracy	O
and	O
efficiency	O
advantages	O
over	O
traditional	O
multiple	B-General_Concept
imputation	I-General_Concept
strategies	O
.	O
</s>
<s>
As	O
alluded	O
in	O
the	O
previous	O
section	O
,	O
single	B-General_Concept
imputation	I-General_Concept
does	O
not	O
take	O
into	O
account	O
the	O
uncertainty	O
in	O
the	O
imputations	B-General_Concept
.	O
</s>
<s>
After	O
imputation	B-General_Concept
,	O
the	O
data	O
is	O
treated	O
as	O
if	O
they	O
were	O
the	O
actual	O
real	O
values	O
in	O
single	B-General_Concept
imputation	I-General_Concept
.	O
</s>
<s>
The	O
negligence	O
of	O
uncertainty	O
in	O
the	O
imputation	B-General_Concept
can	O
lead	O
to	O
overly	O
precise	O
results	O
and	O
errors	O
in	O
any	O
conclusions	O
drawn	O
.	O
</s>
<s>
By	O
imputing	O
multiple	O
times	O
,	O
multiple	B-General_Concept
imputation	I-General_Concept
accounts	O
for	O
the	O
uncertainty	O
and	O
range	O
of	O
values	O
that	O
the	O
true	O
value	O
could	O
have	O
taken	O
.	O
</s>
<s>
As	O
expected	O
,	O
the	O
combination	O
of	O
both	O
uncertainty	O
estimation	O
and	O
deep	O
learning	O
for	O
imputation	B-General_Concept
is	O
among	O
the	O
best	O
strategies	O
and	O
has	O
been	O
used	O
to	O
model	O
heterogeneous	O
drug	O
discovery	O
data	O
.	O
</s>
<s>
Additionally	O
,	O
while	O
single	B-General_Concept
imputation	I-General_Concept
and	O
complete	O
case	O
are	O
easier	O
to	O
implement	O
,	O
multiple	B-General_Concept
imputation	I-General_Concept
is	O
not	O
very	O
difficult	O
to	O
implement	O
.	O
</s>
<s>
There	O
are	O
a	O
wide	O
range	O
of	O
statistical	B-Algorithm
packages	I-Algorithm
in	O
different	B-Algorithm
statistical	I-Algorithm
software	I-Algorithm
that	O
readily	O
performs	O
multiple	B-General_Concept
imputation	I-General_Concept
.	O
</s>
<s>
For	O
example	O
,	O
the	O
MICE	O
package	O
allows	O
users	O
in	O
R	B-Language
to	O
perform	O
multiple	B-General_Concept
imputation	I-General_Concept
using	O
the	O
MICE	O
method	O
.	O
</s>
<s>
MIDAS	O
can	O
be	O
implemented	O
in	O
R	B-Language
with	O
the	O
rMIDAS	O
package	O
and	O
in	O
Python	O
with	O
the	O
MIDASpy	O
package	O
.	O
</s>
