<s>
Multifactor	B-Algorithm
dimensionality	I-Algorithm
reduction	I-Algorithm
(	O
MDR	O
)	O
is	O
a	O
statistical	O
approach	O
,	O
also	O
used	O
in	O
machine	O
learning	O
automatic	O
approaches	O
,	O
for	O
detecting	O
and	O
characterizing	O
combinations	O
of	O
attributes	O
or	O
independent	O
variables	O
that	O
interact	O
to	O
influence	O
a	O
dependent	O
or	O
class	O
variable	O
.	O
</s>
<s>
MDR	O
was	O
designed	O
specifically	O
to	O
identify	O
nonadditive	O
interactions	O
among	O
discrete	O
variables	O
that	O
influence	O
a	O
binary	O
outcome	O
and	O
is	O
considered	O
a	O
nonparametric	B-General_Concept
and	O
model-free	O
alternative	O
to	O
traditional	O
statistical	O
methods	O
such	O
as	O
logistic	O
regression	O
.	O
</s>
<s>
The	O
basis	O
of	O
the	O
MDR	O
method	O
is	O
a	O
constructive	O
induction	O
or	O
feature	B-General_Concept
engineering	I-General_Concept
algorithm	O
that	O
converts	O
two	O
or	O
more	O
variables	O
or	O
attributes	O
to	O
a	O
single	O
attribute	B-General_Concept
.	O
</s>
<s>
This	O
process	O
of	O
constructing	O
a	O
new	O
attribute	B-General_Concept
changes	O
the	O
representation	O
space	O
of	O
the	O
data	O
.	O
</s>
<s>
XOR	O
is	O
a	O
logical	O
operator	O
that	O
is	O
commonly	O
used	O
in	O
data	B-Application
mining	I-Application
and	O
machine	O
learning	O
as	O
an	O
example	O
of	O
a	O
function	O
that	O
is	O
not	O
linearly	O
separable	O
.	O
</s>
<s>
Since	O
0/1	O
<	O
1	O
we	O
encode	O
a	O
new	O
attribute	B-General_Concept
(	O
Z	O
)	O
as	O
a	O
0	O
.	O
</s>
<s>
A	O
nice	O
feature	O
of	O
constructive	O
induction	O
methods	O
such	O
as	O
MDR	O
is	O
the	O
ability	O
to	O
use	O
any	O
data	B-Application
mining	I-Application
or	O
machine	O
learning	O
method	O
to	O
analyze	O
the	O
new	O
representation	O
of	O
the	O
data	O
.	O
</s>
<s>
Decision	B-Algorithm
trees	I-Algorithm
,	O
neural	B-Architecture
networks	I-Architecture
,	O
or	O
a	O
naive	B-General_Concept
Bayes	I-General_Concept
classifier	I-General_Concept
could	O
be	O
used	O
in	O
combination	O
with	O
measures	O
of	O
model	O
quality	O
such	O
as	O
balanced	O
accuracy	O
and	O
mutual	O
information	O
.	O
</s>
<s>
As	O
with	O
any	O
machine	O
learning	O
algorithm	O
there	O
is	O
always	O
concern	O
about	O
overfitting	B-Error_Name
.	O
</s>
<s>
One	O
approach	O
is	O
to	O
estimate	O
the	O
generalizability	O
of	O
a	O
model	O
to	O
independent	O
datasets	O
using	O
methods	O
such	O
as	O
cross-validation	B-Application
.	O
</s>
<s>
Another	O
approach	O
is	O
to	O
generate	O
many	O
random	O
permutations	O
of	O
the	O
data	O
to	O
see	O
what	O
the	O
data	B-Application
mining	I-Application
algorithm	O
finds	O
when	O
given	O
the	O
chance	O
to	O
overfit	B-Error_Name
.	O
</s>
<s>
Permutation	O
testing	O
makes	O
it	O
possible	O
to	O
generate	O
an	O
empirical	O
p-value	B-General_Concept
for	O
the	O
result	O
.	O
</s>
<s>
MDR	O
has	O
mostly	O
been	O
applied	O
to	O
detecting	O
gene-gene	O
interactions	O
or	O
epistasis	O
in	O
genetic	O
studies	O
of	O
common	O
human	O
diseases	O
such	O
as	O
atrial	B-Application
fibrillation	I-Application
,	O
autism	O
,	O
bladder	O
cancer	O
,	O
breast	O
cancer	O
,	O
cardiovascular	O
disease	O
,	O
hypertension	O
,	O
obesity	O
,	O
pancreatic	O
cancer	O
,	O
prostate	O
cancer	O
and	O
tuberculosis	O
.	O
</s>
<s>
A	O
central	O
challenge	O
is	O
the	O
scaling	O
of	O
MDR	O
to	O
big	B-Application
data	I-Application
such	O
as	O
that	O
from	O
genome-wide	O
association	O
studies	O
(	O
GWAS	O
)	O
.	O
</s>
<s>
Another	O
approach	O
is	O
to	O
use	O
stochastic	B-Algorithm
search	I-Algorithm
algorithms	O
such	O
as	O
genetic	B-Algorithm
programming	I-Algorithm
to	O
explore	O
the	O
search	O
space	O
of	O
feature	O
combinations	O
.	O
</s>
<s>
Yet	O
another	O
approach	O
is	O
a	O
brute-force	O
search	O
using	O
high-performance	B-Architecture
computing	I-Architecture
.	O
</s>
<s>
provides	O
an	O
open-source	B-License
and	O
freely-available	O
MDR	O
software	O
package	O
.	O
</s>
