<s>
The	O
structured	O
support-vector	B-Algorithm
machine	I-Algorithm
is	O
a	O
machine	O
learning	O
algorithm	O
that	O
generalizes	O
the	O
Support-Vector	B-Algorithm
Machine	I-Algorithm
(	O
SVM	B-Algorithm
)	O
classifier	O
.	O
</s>
<s>
Whereas	O
the	O
SVM	B-Algorithm
classifier	O
supports	O
binary	B-General_Concept
classification	I-General_Concept
,	O
multiclass	B-General_Concept
classification	I-General_Concept
and	O
regression	O
,	O
the	O
structured	B-Algorithm
SVM	I-Algorithm
allows	O
training	O
of	O
a	O
classifier	O
for	O
general	O
structured	B-General_Concept
output	I-General_Concept
labels	I-General_Concept
.	O
</s>
<s>
After	O
training	O
,	O
the	O
structured	B-Algorithm
SVM	I-Algorithm
model	O
allows	O
one	O
to	O
predict	O
for	O
new	O
sample	O
instances	O
the	O
corresponding	O
output	O
label	O
;	O
that	O
is	O
,	O
given	O
a	O
natural	O
language	O
sentence	O
,	O
the	O
classifier	O
can	O
produce	O
the	O
most	O
likely	O
parse	O
tree	O
.	O
</s>
<s>
For	O
a	O
set	O
of	O
training	O
instances	O
,	O
from	O
a	O
sample	O
space	O
and	O
label	O
space	O
,	O
the	O
structured	B-Algorithm
SVM	I-Algorithm
minimizes	O
the	O
following	O
regularized	O
risk	O
function	O
.	O
</s>
<s>
Because	O
the	O
regularized	O
risk	O
function	O
above	O
is	O
non-differentiable	O
,	O
it	O
is	O
often	O
reformulated	O
in	O
terms	O
of	O
a	O
quadratic	B-Algorithm
program	I-Algorithm
by	O
introducing	O
one	O
slack	O
variable	O
for	O
each	O
sample	O
,	O
each	O
representing	O
the	O
value	O
of	O
the	O
maximum	O
.	O
</s>
<s>
The	O
standard	O
structured	B-Algorithm
SVM	I-Algorithm
primal	O
formulation	O
is	O
given	O
as	O
follows	O
.	O
</s>
<s>
For	O
structured	B-Algorithm
SVMs	I-Algorithm
,	O
given	O
the	O
vector	O
obtained	O
from	O
training	O
,	O
the	O
prediction	O
function	O
is	O
the	O
following	O
.	O
</s>
<s>
The	O
above	O
quadratic	B-Algorithm
program	I-Algorithm
involves	O
a	O
very	O
large	O
,	O
possibly	O
infinite	O
number	O
of	O
linear	O
inequality	O
constraints	O
.	O
</s>
