<s>
Conditional	B-General_Concept
random	I-General_Concept
fields	I-General_Concept
(	O
CRFs	O
)	O
are	O
a	O
class	O
of	O
statistical	O
modeling	O
methods	O
often	O
applied	O
in	O
pattern	O
recognition	O
and	O
machine	O
learning	O
and	O
used	O
for	O
structured	B-General_Concept
prediction	I-General_Concept
.	O
</s>
<s>
Whereas	O
a	O
classifier	B-General_Concept
predicts	O
a	O
label	O
for	O
a	O
single	O
sample	O
without	O
considering	O
"	O
neighbouring	O
"	O
samples	O
,	O
a	O
CRF	O
can	O
take	O
context	O
into	O
account	O
.	O
</s>
<s>
For	O
example	O
,	O
in	O
natural	B-Language
language	I-Language
processing	I-Language
,	O
"	O
linear	O
chain	O
"	O
CRFs	O
are	O
popular	O
,	O
for	O
which	O
each	O
prediction	O
is	O
dependent	O
only	O
on	O
its	O
immediate	O
neighbours	O
.	O
</s>
<s>
Other	O
examples	O
where	O
CRFs	O
are	O
used	O
are	O
:	O
labeling	B-General_Concept
or	O
parsing	B-Language
of	O
sequential	O
data	O
for	O
natural	B-Language
language	I-Language
processing	I-Language
or	O
biological	O
sequences	O
,	O
part-of-speech	O
tagging	O
,	O
shallow	B-General_Concept
parsing	I-General_Concept
,	O
named	B-General_Concept
entity	I-General_Concept
recognition	I-General_Concept
,	O
gene	O
finding	O
,	O
peptide	O
critical	O
functional	O
region	O
finding	O
,	O
and	O
object	O
recognition	O
and	O
image	B-Algorithm
segmentation	I-Algorithm
in	O
computer	B-Application
vision	I-Application
.	O
</s>
<s>
Then	O
is	O
a	O
conditional	B-General_Concept
random	I-General_Concept
field	I-General_Concept
when	O
each	O
random	O
variable	O
,	O
conditioned	O
on	O
,	O
obeys	O
the	O
Markov	O
property	O
with	O
respect	O
to	O
the	O
graph	O
;	O
that	O
is	O
,	O
its	O
probability	O
is	O
dependent	O
only	O
on	O
its	O
neighbours	O
in	O
G	O
:	O
</s>
<s>
The	O
algorithms	O
used	O
in	O
these	O
cases	O
are	O
analogous	O
to	O
the	O
forward-backward	B-Algorithm
and	O
Viterbi	B-Algorithm
algorithm	I-Algorithm
for	O
the	O
case	O
of	O
HMMs	O
.	O
</s>
<s>
If	O
the	O
CRF	O
only	O
contains	O
pair-wise	O
potentials	O
and	O
the	O
energy	O
is	O
submodular	B-Algorithm
,	O
combinatorial	O
min	O
cut/max	O
flow	O
algorithms	O
yield	O
exact	O
solutions	O
.	O
</s>
<s>
It	O
can	O
be	O
solved	O
for	O
example	O
using	O
gradient	B-Algorithm
descent	I-Algorithm
algorithms	O
,	O
or	O
Quasi-Newton	B-Algorithm
methods	I-Algorithm
such	O
as	O
the	O
L-BFGS	B-Algorithm
algorithm	O
.	O
</s>
<s>
There	O
exists	O
another	O
generalization	O
of	O
CRFs	O
,	O
the	O
semi-Markov	O
conditional	B-General_Concept
random	I-General_Concept
field	I-General_Concept
(	O
semi-CRF	O
)	O
,	O
which	O
models	O
variable-length	O
segmentations	B-Algorithm
of	O
the	O
label	O
sequence	O
.	O
</s>
<s>
Finally	O
,	O
large-margin	O
models	O
for	O
structured	B-General_Concept
prediction	I-General_Concept
,	O
such	O
as	O
the	O
structured	B-Algorithm
Support	I-Algorithm
Vector	I-Algorithm
Machine	I-Algorithm
can	O
be	O
seen	O
as	O
an	O
alternative	O
training	O
procedure	O
to	O
CRFs	O
.	O
</s>
<s>
Latent-dynamic	O
conditional	B-General_Concept
random	I-General_Concept
fields	I-General_Concept
(	O
LDCRF	O
)	O
or	O
discriminative	O
probabilistic	O
latent	O
variable	O
models	O
(	O
DPLVM	O
)	O
are	O
a	O
type	O
of	O
CRFs	O
for	O
sequence	O
tagging	O
tasks	O
.	O
</s>
<s>
While	O
LDCRFs	O
can	O
be	O
trained	O
using	O
quasi-Newton	B-Algorithm
methods	I-Algorithm
,	O
a	O
specialized	O
version	O
of	O
the	O
perceptron	B-Algorithm
algorithm	I-Algorithm
called	O
the	O
latent-variable	O
perceptron	B-Algorithm
has	O
been	O
developed	O
for	O
them	O
as	O
well	O
,	O
based	O
on	O
Collins	O
 '	O
structured	O
perceptron	B-Algorithm
algorithm	I-Algorithm
.	O
</s>
<s>
These	O
models	O
find	O
applications	O
in	O
computer	B-Application
vision	I-Application
,	O
specifically	O
gesture	B-General_Concept
recognition	I-General_Concept
from	O
video	O
streams	O
and	O
shallow	B-General_Concept
parsing	I-General_Concept
.	O
</s>
