<s>
The	O
inductive	B-General_Concept
bias	I-General_Concept
(	O
also	O
known	O
as	O
learning	B-General_Concept
bias	I-General_Concept
)	O
of	O
a	O
learning	O
algorithm	O
is	O
the	O
set	O
of	O
assumptions	O
that	O
the	O
learner	O
uses	O
to	O
predict	O
outputs	O
of	O
given	O
inputs	O
that	O
it	O
has	O
not	O
encountered	O
.	O
</s>
<s>
The	O
kind	O
of	O
necessary	O
assumptions	O
about	O
the	O
nature	O
of	O
the	O
target	O
function	O
are	O
subsumed	O
in	O
the	O
phrase	O
inductive	B-General_Concept
bias	I-General_Concept
.	O
</s>
<s>
A	O
classical	O
example	O
of	O
an	O
inductive	B-General_Concept
bias	I-General_Concept
is	O
Occam	O
's	O
razor	O
,	O
assuming	O
that	O
the	O
simplest	O
consistent	O
hypothesis	O
about	O
the	O
target	O
function	O
is	O
actually	O
the	O
best	O
.	O
</s>
<s>
Approaches	O
to	O
a	O
more	O
formal	O
definition	O
of	O
inductive	B-General_Concept
bias	I-General_Concept
are	O
based	O
on	O
mathematical	O
logic	O
.	O
</s>
<s>
Here	O
,	O
the	O
inductive	B-General_Concept
bias	I-General_Concept
is	O
a	O
logical	O
formula	O
that	O
,	O
together	O
with	O
the	O
training	O
data	O
,	O
logically	O
entails	O
the	O
hypothesis	O
generated	O
by	O
the	O
learner	O
.	O
</s>
<s>
However	O
,	O
this	O
strict	O
formalism	O
fails	O
in	O
many	O
practical	O
cases	O
,	O
where	O
the	O
inductive	B-General_Concept
bias	I-General_Concept
can	O
only	O
be	O
given	O
as	O
a	O
rough	O
description	O
(	O
e.g.	O
</s>
<s>
in	O
the	O
case	O
of	O
artificial	B-Architecture
neural	I-Architecture
networks	I-Architecture
)	O
,	O
or	O
not	O
at	O
all	O
.	O
</s>
<s>
This	O
is	O
the	O
bias	O
used	O
in	O
the	O
Naive	B-General_Concept
Bayes	I-General_Concept
classifier	I-General_Concept
.	O
</s>
<s>
Minimum	O
cross-validation	B-Application
error	O
:	O
when	O
trying	O
to	O
choose	O
among	O
hypotheses	O
,	O
select	O
the	O
hypothesis	O
with	O
the	O
lowest	O
cross-validation	B-Application
error	O
.	O
</s>
<s>
Although	O
cross-validation	B-Application
may	O
seem	O
to	O
be	O
free	O
of	O
bias	O
,	O
the	O
"	O
no	O
free	O
lunch	O
"	O
theorems	O
show	O
that	O
cross-validation	B-Application
must	O
be	O
biased	O
.	O
</s>
<s>
This	O
is	O
the	O
bias	O
used	O
in	O
support	B-Algorithm
vector	I-Algorithm
machines	I-Algorithm
.	O
</s>
<s>
This	O
is	O
the	O
assumption	O
behind	O
feature	B-General_Concept
selection	I-General_Concept
algorithms	O
.	O
</s>
<s>
Nearest	B-General_Concept
neighbors	I-General_Concept
:	O
assume	O
that	O
most	O
of	O
the	O
cases	O
in	O
a	O
small	O
neighborhood	O
in	O
feature	O
space	O
belong	O
to	O
the	O
same	O
class	O
.	O
</s>
<s>
This	O
is	O
the	O
bias	O
used	O
in	O
the	O
k-nearest	B-General_Concept
neighbors	I-General_Concept
algorithm	I-General_Concept
.	O
</s>
