<s>
Conformal	B-Algorithm
prediction	I-Algorithm
(	O
CP	O
)	O
is	O
a	O
statistical	O
technique	O
for	O
producing	O
prediction	O
sets	O
without	O
assumptions	O
on	O
the	O
predictive	O
algorithm	O
(	O
often	O
a	O
machine	O
learning	O
system	O
)	O
and	O
only	O
assuming	O
exchangeability	O
of	O
the	O
data	O
.	O
</s>
<s>
A	O
version	O
of	O
CP	O
was	O
first	O
proposed	O
in	O
1998	O
by	O
Gammerman	O
,	O
Vovk	O
,	O
and	O
Vapnik	O
,	O
and	O
since	O
,	O
several	O
variants	O
of	O
conformal	B-Algorithm
prediction	I-Algorithm
have	O
been	O
developed	O
with	O
different	O
computational	O
complexities	O
,	O
formal	O
guarantees	O
,	O
and	O
practical	O
applications	O
.	O
</s>
<s>
Conformal	B-Algorithm
prediction	I-Algorithm
requires	O
a	O
user-specified	O
significance	O
level	O
for	O
which	O
the	O
algorithm	O
should	O
produce	O
its	O
predictions	O
.	O
</s>
<s>
To	O
meet	O
this	O
requirement	O
,	O
the	O
output	O
is	O
a	O
set	O
prediction	O
,	O
instead	O
of	O
a	O
point	O
prediction	O
produced	O
by	O
standard	O
supervised	B-General_Concept
machine	I-General_Concept
learning	I-General_Concept
models	O
.	O
</s>
<s>
For	O
classification	B-General_Concept
tasks	O
,	O
this	O
means	O
that	O
predictions	O
are	O
not	O
a	O
single	O
class	O
,	O
for	O
example	O
'	O
cat	O
 '	O
,	O
but	O
instead	O
a	O
set	O
like	O
{	O
 '	O
cat	O
 '	O
,	O
'	O
dog'}	O
.	O
</s>
<s>
The	O
conformal	B-Algorithm
prediction	I-Algorithm
first	O
arose	O
in	O
a	O
collaboration	O
between	O
Gammerman	O
,	O
Vovk	O
,	O
and	O
Vapnik	O
in	O
1998	O
;	O
this	O
initial	O
version	O
of	O
conformal	B-Algorithm
prediction	I-Algorithm
used	O
E-values	O
,	O
though	O
the	O
version	O
of	O
conformal	B-Algorithm
prediction	I-Algorithm
best	O
known	O
today	O
uses	O
p-values	O
and	O
was	O
proposed	O
a	O
year	O
later	O
by	O
Saunders	O
et	O
al	O
.	O
</s>
<s>
Vovk	O
,	O
Gammerman	O
,	O
and	O
their	O
students	O
and	O
collaborators	O
,	O
particularly	O
Craig	O
Saunders	O
,	O
Harris	O
Papadopoulos	O
,	O
and	O
Kostas	O
Proedrou	O
,	O
continued	O
to	O
develop	O
the	O
ideas	O
of	O
conformal	B-Algorithm
prediction	I-Algorithm
;	O
major	O
developments	O
include	O
the	O
proposal	O
of	O
inductive	O
conformal	B-Algorithm
prediction	I-Algorithm
(	O
a.k.a.	O
</s>
<s>
split	O
conformal	B-Algorithm
prediction	I-Algorithm
)	O
,	O
in	O
2002	O
.	O
</s>
<s>
For	O
conformal	B-Algorithm
prediction	I-Algorithm
,	O
a	O
n%	O
prediction	O
region	O
is	O
said	O
to	O
be	O
valid	O
if	O
the	O
truth	O
is	O
in	O
the	O
output	O
n%	O
of	O
the	O
time	O
.	O
</s>
<s>
For	O
classification	B-General_Concept
,	O
this	O
size	O
is	O
the	O
number	O
of	O
classes	O
;	O
for	O
regression	O
,	O
it	O
is	O
interval	O
width	O
.	O
</s>
<s>
In	O
the	O
purest	O
form	O
,	O
conformal	B-Algorithm
prediction	I-Algorithm
is	O
made	O
for	O
an	O
online	O
(	O
transductive	B-General_Concept
)	O
section	O
.	O
</s>
<s>
Thus	O
,	O
the	O
underlying	O
model	O
can	O
be	O
re-trained	O
using	O
this	O
new	O
data	O
point	O
and	O
the	O
next	O
prediction	O
will	O
be	O
made	O
on	O
a	O
calibration	B-General_Concept
set	O
containing	O
n+1	O
data	O
points	O
,	O
where	O
the	O
previous	O
model	O
had	O
n	O
data	O
points	O
.	O
</s>
<s>
The	O
goal	O
of	O
standard	O
classification	B-General_Concept
algorithms	O
is	O
to	O
classify	O
a	O
test	O
object	O
into	O
one	O
of	O
several	O
discrete	O
classes	O
.	O
</s>
<s>
Conformal	O
classifiers	B-General_Concept
instead	O
compute	O
and	O
output	O
the	O
p-value	O
for	O
each	O
available	O
class	O
by	O
performing	O
a	O
ranking	O
of	O
the	O
nonconformity	O
measure	O
(α-	O
value	O
)	O
of	O
the	O
test	O
object	O
against	O
examples	O
from	O
the	O
training	O
data	O
set	O
.	O
</s>
<s>
Transductive	B-General_Concept
algorithms	O
compute	O
the	O
nonconformity	O
score	O
using	O
all	O
available	O
training	O
data	O
,	O
while	O
inductive	O
algorithms	O
compute	O
it	O
on	O
a	O
subset	O
of	O
the	O
training	O
set	O
.	O
</s>
<s>
Inductive	O
Conformal	B-Algorithm
Prediction	I-Algorithm
was	O
first	O
known	O
as	O
inductive	O
confidence	O
machines	O
,	O
but	O
was	O
later	O
re-introduced	O
as	O
ICP	O
.	O
</s>
<s>
Conformal	B-Algorithm
prediction	I-Algorithm
was	O
initially	O
formulated	O
for	O
the	O
task	O
of	O
classification	B-General_Concept
,	O
but	O
was	O
later	O
modified	O
for	O
regression	O
.	O
</s>
<s>
Unlike	O
classification	B-General_Concept
,	O
which	O
outputs	O
p-values	O
without	O
a	O
given	O
significance	O
level	O
,	O
regression	O
requires	O
a	O
fixed	O
significance	O
level	O
at	O
prediction	O
time	O
in	O
order	O
to	O
produce	O
prediction	O
intervals	O
for	O
a	O
new	O
test	O
object	O
.	O
</s>
<s>
For	O
classic	O
conformal	O
regression	O
,	O
there	O
is	O
no	O
transductive	B-General_Concept
algorithm	O
.	O
</s>
<s>
All	O
inductive	O
algorithms	O
require	O
splitting	O
the	O
available	O
training	O
examples	O
into	O
two	O
disjoint	O
sets	O
:	O
one	O
set	O
used	O
for	O
training	O
the	O
underlying	O
model	O
(	O
the	O
proper	O
training	O
set	O
)	O
and	O
one	O
set	O
for	O
calibrating	O
the	O
prediction	O
(	O
the	O
calibration	B-General_Concept
set	O
)	O
.	O
</s>
<s>
A	O
common	O
type	O
of	O
SCPs	O
is	O
the	O
cross-conformal	O
predictor	O
(	O
CCP	O
)	O
,	O
which	O
splits	O
the	O
training	O
data	O
into	O
proper	O
training	O
and	O
calibration	B-General_Concept
sets	O
multiple	O
times	O
in	O
a	O
strategy	O
similar	O
to	O
k-fold	O
cross-validation	O
.	O
</s>
<s>
Several	O
machine	O
learning	O
models	O
can	O
be	O
used	O
in	O
conjunction	O
with	O
conformal	B-Algorithm
prediction	I-Algorithm
.	O
</s>
<s>
Studies	O
have	O
shown	O
that	O
it	O
can	O
be	O
applied	O
to	O
for	O
example	O
convolutional	B-Architecture
neural	I-Architecture
networks	I-Architecture
,	O
support-vector	B-Algorithm
machines	I-Algorithm
and	O
others	O
.	O
</s>
<s>
Conformal	B-Algorithm
prediction	I-Algorithm
is	O
used	O
in	O
a	O
variety	O
of	O
fields	O
and	O
is	O
an	O
active	O
area	O
of	O
research	O
.	O
</s>
<s>
Within	O
language	O
technology	O
,	O
conformal	B-Algorithm
prediction	I-Algorithm
papers	O
are	O
routinely	O
presented	O
at	O
COPA	O
.	O
</s>
<s>
Conformal	B-Algorithm
prediction	I-Algorithm
is	O
one	O
of	O
the	O
main	O
subjects	O
discussed	O
during	O
the	O
COPA	O
conference	O
each	O
year	O
.	O
</s>
<s>
Both	O
theory	O
and	O
applications	O
of	O
conformal	B-Algorithm
predictions	I-Algorithm
are	O
presented	O
by	O
leaders	O
of	O
the	O
field	O
.	O
</s>
