<s>
Decision	B-Algorithm
tree	I-Algorithm
learning	I-Algorithm
is	O
a	O
supervised	O
learning	O
approach	O
used	O
in	O
statistics	O
,	O
data	B-Application
mining	I-Application
and	O
machine	O
learning	O
.	O
</s>
<s>
In	O
this	O
formalism	O
,	O
a	O
classification	B-General_Concept
or	O
regression	O
decision	B-Algorithm
tree	I-Algorithm
is	O
used	O
as	O
a	O
predictive	B-General_Concept
model	I-General_Concept
to	O
draw	O
conclusions	O
about	O
a	O
set	O
of	O
observations	O
.	O
</s>
<s>
Tree	O
models	O
where	O
the	O
target	O
variable	O
can	O
take	O
a	O
discrete	O
set	O
of	O
values	O
are	O
called	O
classification	B-Algorithm
trees	I-Algorithm
;	O
in	O
these	O
tree	O
structures	O
,	O
leaves	B-Data_Structure
represent	O
class	O
labels	O
and	O
branches	O
represent	O
conjunctions	O
of	O
features	O
that	O
lead	O
to	O
those	O
class	O
labels	O
.	O
</s>
<s>
Decision	B-Algorithm
trees	I-Algorithm
where	O
the	O
target	O
variable	O
can	O
take	O
continuous	O
values	O
(	O
typically	O
real	O
numbers	O
)	O
are	O
called	O
regression	B-Algorithm
trees	I-Algorithm
.	O
</s>
<s>
More	O
generally	O
,	O
the	O
concept	O
of	O
regression	B-Algorithm
tree	I-Algorithm
can	O
be	O
extended	O
to	O
any	O
kind	O
of	O
object	O
equipped	O
with	O
pairwise	O
dissimilarities	O
such	O
as	O
categorical	O
sequences	O
.	O
</s>
<s>
Decision	B-Algorithm
trees	I-Algorithm
are	O
among	O
the	O
most	O
popular	O
machine	O
learning	O
algorithms	O
given	O
their	O
intelligibility	O
and	O
simplicity	O
.	O
</s>
<s>
In	O
decision	O
analysis	O
,	O
a	O
decision	B-Algorithm
tree	I-Algorithm
can	O
be	O
used	O
to	O
visually	O
and	O
explicitly	O
represent	O
decisions	O
and	O
decision	O
making	O
.	O
</s>
<s>
In	O
data	B-Application
mining	I-Application
,	O
a	O
decision	B-Algorithm
tree	I-Algorithm
describes	O
data	O
(	O
but	O
the	O
resulting	O
classification	B-Algorithm
tree	I-Algorithm
can	O
be	O
an	O
input	O
for	O
decision	O
making	O
)	O
.	O
</s>
<s>
Decision	B-Algorithm
tree	I-Algorithm
learning	I-Algorithm
is	O
a	O
method	O
commonly	O
used	O
in	O
data	B-Application
mining	I-Application
.	O
</s>
<s>
A	O
decision	B-Algorithm
tree	I-Algorithm
is	O
a	O
simple	O
representation	O
for	O
classifying	O
examples	O
.	O
</s>
<s>
For	O
this	O
section	O
,	O
assume	O
that	O
all	O
of	O
the	O
input	O
features	O
have	O
finite	O
discrete	O
domains	O
,	O
and	O
there	O
is	O
a	O
single	O
target	O
feature	B-Algorithm
called	O
the	O
"	O
classification	B-General_Concept
"	O
.	O
</s>
<s>
Each	O
element	O
of	O
the	O
domain	O
of	O
the	O
classification	B-General_Concept
is	O
called	O
a	O
class	O
.	O
</s>
<s>
A	O
decision	B-Algorithm
tree	I-Algorithm
or	O
a	O
classification	B-Algorithm
tree	I-Algorithm
is	O
a	O
tree	O
in	O
which	O
each	O
internal	O
(	O
non-leaf	O
)	O
node	O
is	O
labeled	O
with	O
an	O
input	O
feature	B-Algorithm
.	O
</s>
<s>
The	O
arcs	O
coming	O
from	O
a	O
node	O
labeled	O
with	O
an	O
input	O
feature	B-Algorithm
are	O
labeled	O
with	O
each	O
of	O
the	O
possible	O
values	O
of	O
the	O
target	O
feature	B-Algorithm
or	O
the	O
arc	O
leads	O
to	O
a	O
subordinate	O
decision	O
node	O
on	O
a	O
different	O
input	O
feature	B-Algorithm
.	O
</s>
<s>
Each	O
leaf	O
of	O
the	O
tree	O
is	O
labeled	O
with	O
a	O
class	O
or	O
a	O
probability	O
distribution	O
over	O
the	O
classes	O
,	O
signifying	O
that	O
the	O
data	O
set	O
has	O
been	O
classified	O
by	O
the	O
tree	O
into	O
either	O
a	O
specific	O
class	O
,	O
or	O
into	O
a	O
particular	O
probability	O
distribution	O
(	O
which	O
,	O
if	O
the	O
decision	B-Algorithm
tree	I-Algorithm
is	O
well-constructed	O
,	O
is	O
skewed	O
towards	O
certain	O
subsets	O
of	O
classes	O
)	O
.	O
</s>
<s>
The	O
splitting	O
is	O
based	O
on	O
a	O
set	O
of	O
splitting	O
rules	O
based	O
on	O
classification	B-General_Concept
features	O
.	O
</s>
<s>
This	O
process	O
is	O
repeated	O
on	O
each	O
derived	O
subset	O
in	O
a	O
recursive	O
manner	O
called	O
recursive	B-General_Concept
partitioning	I-General_Concept
.	O
</s>
<s>
This	O
process	O
of	O
top-down	O
induction	O
of	O
decision	B-Algorithm
trees	I-Algorithm
(	O
TDIDT	O
)	O
is	O
an	O
example	O
of	O
a	O
greedy	B-Algorithm
algorithm	I-Algorithm
,	O
and	O
it	O
is	O
by	O
far	O
the	O
most	O
common	O
strategy	O
for	O
learning	O
decision	B-Algorithm
trees	I-Algorithm
from	O
data	O
.	O
</s>
<s>
In	O
data	B-Application
mining	I-Application
,	O
decision	B-Algorithm
trees	I-Algorithm
can	O
be	O
described	O
also	O
as	O
the	O
combination	O
of	O
mathematical	O
and	O
computational	O
techniques	O
to	O
aid	O
the	O
description	O
,	O
categorization	O
and	O
generalization	O
of	O
a	O
given	O
set	O
of	O
data	O
.	O
</s>
<s>
Decision	B-Algorithm
trees	I-Algorithm
used	O
in	O
data	B-Application
mining	I-Application
are	O
of	O
two	O
main	O
types	O
:	O
</s>
<s>
Classification	B-Algorithm
tree	I-Algorithm
analysis	O
is	O
when	O
the	O
predicted	O
outcome	O
is	O
the	O
class	O
(	O
discrete	O
)	O
to	O
which	O
the	O
data	O
belongs	O
.	O
</s>
<s>
Regression	B-Algorithm
tree	I-Algorithm
analysis	O
is	O
when	O
the	O
predicted	O
outcome	O
can	O
be	O
considered	O
a	O
real	O
number	O
(	O
e.g.	O
</s>
<s>
The	O
term	O
classification	B-Algorithm
and	I-Algorithm
regression	I-Algorithm
tree	I-Algorithm
(	O
CART	O
)	O
analysis	O
is	O
an	O
umbrella	O
term	O
used	O
to	O
refer	O
to	O
either	O
of	O
the	O
above	O
procedures	O
,	O
first	O
introduced	O
by	O
Breiman	O
et	O
al	O
.	O
</s>
<s>
Trees	B-Algorithm
used	O
for	O
regression	O
and	O
trees	B-Algorithm
used	O
for	O
classification	B-General_Concept
have	O
some	O
similarities	O
–	O
but	O
also	O
some	O
differences	O
,	O
such	O
as	O
the	O
procedure	O
used	O
to	O
determine	O
where	O
to	O
split	O
.	O
</s>
<s>
Some	O
techniques	O
,	O
often	O
called	O
ensemble	O
methods	O
,	O
construct	O
more	O
than	O
one	O
decision	B-Algorithm
tree	I-Algorithm
:	O
</s>
<s>
Boosted	O
trees	B-Algorithm
Incrementally	O
building	O
an	O
ensemble	O
by	O
training	O
each	O
new	O
instance	O
to	O
emphasize	O
the	O
training	O
instances	O
previously	O
mis-modeled	O
.	O
</s>
<s>
A	O
typical	O
example	O
is	O
AdaBoost	B-Algorithm
.	O
</s>
<s>
These	O
can	O
be	O
used	O
for	O
regression-type	O
and	O
classification-type	O
problems	O
.	O
</s>
<s>
Bootstrap	B-Algorithm
aggregated	I-Algorithm
(	O
or	O
bagged	O
)	O
decision	B-Algorithm
trees	I-Algorithm
,	O
an	O
early	O
ensemble	O
method	O
,	O
builds	O
multiple	O
decision	B-Algorithm
trees	I-Algorithm
by	O
repeatedly	O
resampling	B-Application
training	I-Application
data	I-Application
with	I-Application
replacement	I-Application
,	O
and	O
voting	O
the	O
trees	B-Algorithm
for	O
a	O
consensus	O
prediction	O
.	O
</s>
<s>
Rotation	O
forest	O
–	O
in	O
which	O
every	O
decision	B-Algorithm
tree	I-Algorithm
is	O
trained	O
by	O
first	O
applying	O
principal	B-Application
component	I-Application
analysis	I-Application
(	O
PCA	O
)	O
on	O
a	O
random	O
subset	O
of	O
the	O
input	O
features	O
.	O
</s>
<s>
A	O
special	O
case	O
of	O
a	O
decision	B-Algorithm
tree	I-Algorithm
is	O
a	O
decision	B-General_Concept
list	I-General_Concept
,	O
which	O
is	O
a	O
one-sided	O
decision	B-Algorithm
tree	I-Algorithm
,	O
so	O
that	O
every	O
internal	O
node	O
has	O
exactly	O
1	O
leaf	B-Data_Structure
node	I-Data_Structure
and	O
exactly	O
1	O
internal	O
node	O
as	O
a	O
child	O
(	O
except	O
for	O
the	O
bottommost	O
node	O
,	O
whose	O
only	O
child	O
is	O
a	O
single	O
leaf	B-Data_Structure
node	I-Data_Structure
)	O
.	O
</s>
<s>
While	O
less	O
expressive	O
,	O
decision	B-General_Concept
lists	I-General_Concept
are	O
arguably	O
easier	O
to	O
understand	O
than	O
general	O
decision	B-Algorithm
trees	I-Algorithm
due	O
to	O
their	O
added	O
sparsity	O
,	O
permit	O
non-greedy	O
learning	O
methods	O
and	O
monotonic	O
constraints	O
to	O
be	O
imposed	O
.	O
</s>
<s>
Notable	O
decision	B-Algorithm
tree	I-Algorithm
algorithms	O
include	O
:	O
</s>
<s>
Chi-square	B-General_Concept
automatic	I-General_Concept
interaction	I-General_Concept
detection	I-General_Concept
(	O
CHAID	B-General_Concept
)	O
.	O
</s>
<s>
Performs	O
multi-level	O
splits	O
when	O
computing	O
classification	B-Algorithm
trees	I-Algorithm
.	O
</s>
<s>
MARS	B-General_Concept
:	O
extends	O
decision	B-Algorithm
trees	I-Algorithm
to	O
handle	O
numerical	O
data	O
better	O
.	O
</s>
<s>
Conditional	O
Inference	O
Trees	B-Algorithm
.	O
</s>
<s>
Statistics-based	O
approach	O
that	O
uses	O
non-parametric	O
tests	O
as	O
splitting	O
criteria	O
,	O
corrected	O
for	O
multiple	O
testing	O
to	O
avoid	O
overfitting	B-Error_Name
.	O
</s>
<s>
This	O
approach	O
results	O
in	O
unbiased	O
predictor	O
selection	O
and	O
does	O
not	O
require	O
pruning	B-Algorithm
.	O
</s>
<s>
ID3	B-Algorithm
and	O
CART	O
were	O
invented	O
independently	O
at	O
around	O
the	O
same	O
time	O
(	O
between	O
1970	O
and	O
1980	O
)	O
,	O
yet	O
follow	O
a	O
similar	O
approach	O
for	O
learning	O
a	O
decision	B-Algorithm
tree	I-Algorithm
from	O
training	O
tuples	O
.	O
</s>
<s>
It	O
has	O
also	O
been	O
proposed	O
to	O
leverage	O
concepts	O
of	O
fuzzy	O
set	O
theory	O
for	O
the	O
definition	O
of	O
a	O
special	O
version	O
of	O
decision	B-Algorithm
tree	I-Algorithm
,	O
known	O
as	O
Fuzzy	O
Decision	B-Algorithm
Tree	I-Algorithm
(	O
FDT	O
)	O
.	O
</s>
<s>
In	O
this	O
type	O
of	O
fuzzy	O
classification	B-General_Concept
,	O
generally	O
,	O
an	O
input	O
vector	O
is	O
associated	O
with	O
multiple	O
classes	O
,	O
each	O
with	O
a	O
different	O
confidence	O
value	O
.	O
</s>
<s>
Boosted	O
ensembles	O
of	O
FDTs	O
have	O
been	O
recently	O
investigated	O
as	O
well	O
,	O
and	O
they	O
have	O
shown	O
performances	O
comparable	O
to	O
those	O
of	O
other	O
very	O
efficient	O
fuzzy	O
classifiers	B-General_Concept
.	O
</s>
<s>
Algorithms	O
for	O
constructing	O
decision	B-Algorithm
trees	I-Algorithm
usually	O
work	O
top-down	O
,	O
by	O
choosing	O
a	O
variable	O
at	O
each	O
step	O
that	O
best	O
splits	O
the	O
set	O
of	O
items	O
.	O
</s>
<s>
Depending	O
on	O
the	O
underlying	O
metric	O
,	O
the	O
performance	O
of	O
various	O
heuristic	O
algorithms	O
for	O
decision	B-Algorithm
tree	I-Algorithm
learning	I-Algorithm
may	O
vary	O
significantly	O
.	O
</s>
<s>
A	O
simple	O
and	O
effective	O
metric	O
can	O
be	O
used	O
to	O
identify	O
the	O
degree	O
to	O
which	O
true	O
positives	O
outweigh	O
true	O
negatives	O
(	O
see	O
Confusion	B-General_Concept
matrix	I-General_Concept
)	O
.	O
</s>
<s>
The	O
resulting	O
number	O
gives	O
an	O
estimate	O
on	O
how	O
many	O
positive	O
examples	O
the	O
feature	B-Algorithm
could	O
correctly	O
identify	O
within	O
the	O
data	O
,	O
with	O
higher	O
numbers	O
meaning	O
that	O
the	O
feature	B-Algorithm
could	O
correctly	O
classify	O
more	O
positive	O
samples	O
.	O
</s>
<s>
Below	O
is	O
an	O
example	O
of	O
how	O
to	O
use	O
the	O
metric	O
when	O
the	O
full	O
confusion	B-General_Concept
matrix	I-General_Concept
of	O
a	O
certain	O
feature	B-Algorithm
is	O
given	O
:	O
</s>
<s>
This	O
means	O
that	O
using	O
the	O
estimate	O
on	O
this	O
feature	B-Algorithm
would	O
have	O
it	O
receive	O
a	O
score	O
of	O
6	O
.	O
</s>
<s>
For	O
example	O
,	O
if	O
two	O
features	O
both	O
had	O
a	O
FP	O
value	O
of	O
2	O
while	O
one	O
of	O
the	O
features	O
had	O
a	O
higher	O
TP	O
value	O
,	O
that	O
feature	B-Algorithm
would	O
be	O
ranked	O
higher	O
than	O
the	O
other	O
because	O
the	O
resulting	O
estimate	O
when	O
using	O
the	O
equation	O
would	O
give	O
a	O
higher	O
value	O
.	O
</s>
<s>
To	O
combat	O
this	O
,	O
one	O
could	O
use	O
a	O
more	O
powerful	O
metric	O
known	O
as	O
Sensitivity	O
that	O
takes	O
into	O
account	O
the	O
proportions	O
of	O
the	O
values	O
from	O
the	O
confusion	B-General_Concept
matrix	I-General_Concept
to	O
give	O
the	O
actual	O
true	O
positive	O
rate	O
(	O
TPR	O
)	O
.	O
</s>
<s>
In	O
this	O
example	O
,	O
Feature	B-Algorithm
A	O
had	O
an	O
estimate	O
of	O
6	O
and	O
a	O
TPR	O
of	O
approximately	O
0.73	O
while	O
Feature	B-Algorithm
B	O
had	O
an	O
estimate	O
of	O
4	O
and	O
a	O
TPR	O
of	O
0.75	O
.	O
</s>
<s>
This	O
shows	O
that	O
although	O
the	O
positive	O
estimate	O
for	O
some	O
feature	B-Algorithm
may	O
be	O
higher	O
,	O
the	O
more	O
accurate	O
TPR	O
value	O
for	O
that	O
feature	B-Algorithm
may	O
be	O
lower	O
when	O
compared	O
to	O
other	O
features	O
that	O
have	O
a	O
lower	O
positive	O
estimate	O
.	O
</s>
<s>
Depending	O
on	O
the	O
situation	O
and	O
knowledge	O
of	O
the	O
data	O
and	O
decision	B-Algorithm
trees	I-Algorithm
,	O
one	O
may	O
opt	O
to	O
use	O
the	O
positive	O
estimate	O
for	O
a	O
quick	O
and	O
easy	O
solution	O
to	O
their	O
problem	O
.	O
</s>
<s>
Gini	O
impurity	O
,	O
Gini	O
's	O
diversity	O
index	O
,	O
or	O
Gini-Simpson	O
Index	O
in	O
biodiversity	O
research	O
,	O
is	O
named	O
after	O
Italian	O
mathematician	O
Corrado	O
Gini	O
and	O
used	O
by	O
the	O
CART	O
(	O
classification	B-Algorithm
and	I-Algorithm
regression	I-Algorithm
tree	I-Algorithm
)	O
algorithm	O
for	O
classification	B-Algorithm
trees	I-Algorithm
.	O
</s>
<s>
In	O
this	O
sense	O
,	O
the	O
Gini	O
impurity	O
is	O
nothing	O
but	O
a	O
variation	O
of	O
the	O
usual	O
entropy	O
measure	O
for	O
decision	B-Algorithm
trees	I-Algorithm
.	O
</s>
<s>
Used	O
by	O
the	O
ID3	B-Algorithm
,	O
C4.5	B-Algorithm
and	O
C5.0	O
tree-generation	O
algorithms	O
.	O
</s>
<s>
Information	B-Algorithm
gain	I-Algorithm
is	O
based	O
on	O
the	O
concept	O
of	O
entropy	O
and	O
information	O
content	O
from	O
information	O
theory	O
.	O
</s>
<s>
That	O
is	O
,	O
the	O
expected	O
information	B-Algorithm
gain	I-Algorithm
is	O
the	O
mutual	O
information	O
,	O
meaning	O
that	O
on	O
average	O
,	O
the	O
reduction	O
in	O
the	O
entropy	O
of	O
T	O
is	O
the	O
mutual	O
information	O
.	O
</s>
<s>
Information	B-Algorithm
gain	I-Algorithm
is	O
used	O
to	O
decide	O
which	O
feature	B-Algorithm
to	O
split	O
on	O
at	O
each	O
step	O
in	O
building	O
the	O
tree	O
.	O
</s>
<s>
To	O
construct	O
a	O
decision	B-Algorithm
tree	I-Algorithm
on	O
this	O
data	O
,	O
we	O
need	O
to	O
compare	O
the	O
information	B-Algorithm
gain	I-Algorithm
of	O
each	O
of	O
four	O
trees	B-Algorithm
,	O
each	O
split	O
on	O
one	O
of	O
the	O
four	O
features	O
.	O
</s>
<s>
The	O
split	O
with	O
the	O
highest	O
information	B-Algorithm
gain	I-Algorithm
will	O
be	O
taken	O
as	O
the	O
first	O
split	O
and	O
the	O
process	O
will	O
continue	O
until	O
all	O
children	O
nodes	O
each	O
have	O
consistent	O
data	O
,	O
or	O
until	O
the	O
information	B-Algorithm
gain	I-Algorithm
is	O
0	O
.	O
</s>
<s>
To	O
find	O
the	O
information	B-Algorithm
gain	I-Algorithm
of	O
the	O
split	O
using	O
windy	O
,	O
we	O
must	O
first	O
calculate	O
the	O
information	O
in	O
the	O
data	O
before	O
the	O
split	O
.	O
</s>
<s>
The	O
split	O
using	O
the	O
feature	B-Algorithm
windy	O
results	O
in	O
two	O
children	O
nodes	O
,	O
one	O
for	O
a	O
windy	O
value	O
of	O
true	O
and	O
one	O
for	O
a	O
windy	O
value	O
of	O
false	O
.	O
</s>
<s>
Now	O
we	O
can	O
calculate	O
the	O
information	B-Algorithm
gain	I-Algorithm
achieved	O
by	O
splitting	O
on	O
the	O
windy	O
feature	B-Algorithm
.	O
</s>
<s>
To	O
build	O
the	O
tree	O
,	O
the	O
information	B-Algorithm
gain	I-Algorithm
of	O
each	O
possible	O
first	O
split	O
would	O
need	O
to	O
be	O
calculated	O
.	O
</s>
<s>
The	O
best	O
first	O
split	O
is	O
the	O
one	O
that	O
provides	O
the	O
most	O
information	B-Algorithm
gain	I-Algorithm
.	O
</s>
<s>
Information	B-Algorithm
gain	I-Algorithm
is	O
also	O
known	O
as	O
Shannon	O
index	O
in	O
bio	O
diversity	O
research	O
.	O
</s>
<s>
Introduced	O
in	O
CART	O
,	O
variance	O
reduction	O
is	O
often	O
employed	O
in	O
cases	O
where	O
the	O
target	O
variable	O
is	O
continuous	O
(	O
regression	B-Algorithm
tree	I-Algorithm
)	O
,	O
meaning	O
that	O
use	O
of	O
many	O
other	O
metrics	O
would	O
first	O
require	O
discretization	O
before	O
being	O
applied	O
.	O
</s>
<s>
To	O
start	O
a	O
decision	B-Algorithm
tree	I-Algorithm
,	O
we	O
will	O
calculate	O
the	O
maximum	O
value	O
of	O
using	O
each	O
feature	B-Algorithm
to	O
find	O
which	O
one	O
will	O
split	O
the	O
root	O
node	O
.	O
</s>
<s>
To	O
find	O
of	O
the	O
feature	B-Algorithm
savings	O
,	O
we	O
need	O
to	O
note	O
the	O
quantity	O
of	O
each	O
value	O
.	O
</s>
<s>
Compared	O
to	O
other	O
metrics	O
such	O
as	O
information	B-Algorithm
gain	I-Algorithm
,	O
the	O
measure	O
of	O
"	O
goodness	O
"	O
will	O
attempt	O
to	O
create	O
a	O
more	O
balanced	O
tree	O
,	O
leading	O
to	O
more-consistent	O
decision	O
time	O
.	O
</s>
<s>
Amongst	O
other	O
data	B-Application
mining	I-Application
methods	O
,	O
decision	B-Algorithm
trees	I-Algorithm
have	O
various	O
advantages	O
:	O
</s>
<s>
People	O
are	O
able	O
to	O
understand	O
decision	B-Algorithm
tree	I-Algorithm
models	O
after	O
a	O
brief	O
explanation	O
.	O
</s>
<s>
Trees	B-Algorithm
can	O
also	O
be	O
displayed	O
graphically	O
in	O
a	O
way	O
that	O
is	O
easy	O
for	O
non-experts	O
to	O
interpret	O
.	O
</s>
<s>
(	O
For	O
example	O
,	O
relation	O
rules	O
can	O
be	O
used	O
only	O
with	O
nominal	O
variables	O
while	O
neural	B-Architecture
networks	I-Architecture
can	O
be	O
used	O
only	O
with	O
numerical	O
variables	O
or	O
categoricals	O
converted	O
to	O
0-1	O
values	O
.	O
)	O
</s>
<s>
Early	O
decision	B-Algorithm
trees	I-Algorithm
were	O
only	O
capable	O
of	O
handling	O
categorical	O
variables	O
,	O
but	O
more	O
recent	O
versions	O
,	O
such	O
as	O
C4.5	B-Algorithm
,	O
do	O
not	O
have	O
this	O
limitation	O
.	O
</s>
<s>
Since	O
trees	B-Algorithm
can	O
handle	O
qualitative	O
predictors	O
,	O
there	O
is	O
no	O
need	O
to	O
create	O
dummy	O
variables	O
.	O
</s>
<s>
Uses	O
a	O
white	B-General_Concept
box	I-General_Concept
or	O
open-box	O
model	O
.	O
</s>
<s>
By	O
contrast	O
,	O
in	O
a	O
black	B-Device
box	I-Device
model	O
,	O
the	O
explanation	O
for	O
the	O
results	O
is	O
typically	O
difficult	O
to	O
understand	O
,	O
for	O
example	O
with	O
an	O
artificial	B-Architecture
neural	I-Architecture
network	I-Architecture
.	O
</s>
<s>
In	O
built	O
feature	B-General_Concept
selection	I-General_Concept
.	O
</s>
<s>
Additional	O
irrelevant	O
feature	B-Algorithm
will	O
be	O
less	O
used	O
so	O
that	O
they	O
can	O
be	O
removed	O
on	O
subsequent	O
runs	O
.	O
</s>
<s>
The	O
hierarchy	O
of	O
attributes	O
in	O
a	O
decision	B-Algorithm
tree	I-Algorithm
reflects	O
the	O
importance	O
of	O
attributes	O
.	O
</s>
<s>
Decision	B-Algorithm
trees	I-Algorithm
can	O
approximate	O
any	O
Boolean	O
function	O
e.g.	O
</s>
<s>
Trees	B-Algorithm
can	O
be	O
very	O
non-robust	O
.	O
</s>
<s>
The	O
problem	O
of	O
learning	O
an	O
optimal	O
decision	B-Algorithm
tree	I-Algorithm
is	O
known	O
to	O
be	O
NP-complete	O
under	O
several	O
aspects	O
of	O
optimality	O
and	O
even	O
for	O
simple	O
concepts	O
.	O
</s>
<s>
Consequently	O
,	O
practical	O
decision-tree	B-Algorithm
learning	O
algorithms	O
are	O
based	O
on	O
heuristics	O
such	O
as	O
the	O
greedy	B-Algorithm
algorithm	I-Algorithm
where	O
locally	O
optimal	O
decisions	O
are	O
made	O
at	O
each	O
node	O
.	O
</s>
<s>
Such	O
algorithms	O
cannot	O
guarantee	O
to	O
return	O
the	O
globally	O
optimal	O
decision	B-Algorithm
tree	I-Algorithm
.	O
</s>
<s>
Decision-tree	B-Algorithm
learners	O
can	O
create	O
over-complex	O
trees	B-Algorithm
that	O
do	O
not	O
generalize	O
well	O
from	O
the	O
training	O
data	O
.	O
</s>
<s>
(	O
This	O
is	O
known	O
as	O
overfitting	B-Error_Name
.	O
)	O
</s>
<s>
Mechanisms	O
such	O
as	O
pruning	B-Algorithm
are	O
necessary	O
to	O
avoid	O
this	O
problem	O
(	O
with	O
the	O
exception	O
of	O
some	O
algorithms	O
such	O
as	O
the	O
Conditional	O
Inference	O
approach	O
,	O
that	O
does	O
not	O
require	O
pruning	B-Algorithm
)	O
.	O
</s>
<s>
The	O
average	O
depth	O
of	O
the	O
tree	O
that	O
is	O
defined	O
by	O
the	O
number	O
of	O
nodes	O
or	O
tests	O
till	O
classification	B-General_Concept
is	O
not	O
guaranteed	O
to	O
be	O
minimal	O
or	O
small	O
under	O
various	O
splitting	O
criteria	O
.	O
</s>
<s>
For	O
data	O
including	O
categorical	O
variables	O
with	O
different	O
numbers	O
of	O
levels	O
,	O
information	B-Algorithm
gain	I-Algorithm
in	I-Algorithm
decision	I-Algorithm
trees	I-Algorithm
is	O
biased	O
in	O
favor	O
of	O
attributes	O
with	O
more	O
levels	O
.	O
</s>
<s>
To	O
counter	O
this	O
problem	O
,	O
instead	O
of	O
choosing	O
the	O
attribute	O
with	O
highest	O
information	B-Algorithm
gain	I-Algorithm
,	O
one	O
can	O
choose	O
the	O
attribute	O
with	O
the	O
highest	O
information	B-General_Concept
gain	I-General_Concept
ratio	I-General_Concept
among	O
the	O
attributes	O
whose	O
information	B-Algorithm
gain	I-Algorithm
is	O
greater	O
than	O
the	O
mean	O
information	B-Algorithm
gain	I-Algorithm
.	O
</s>
<s>
This	O
biases	O
the	O
decision	B-Algorithm
tree	I-Algorithm
against	O
considering	O
attributes	O
with	O
a	O
large	O
number	O
of	O
distinct	O
values	O
,	O
while	O
not	O
giving	O
an	O
unfair	O
advantage	O
to	O
attributes	O
with	O
very	O
low	O
information	B-Algorithm
gain	I-Algorithm
.	O
</s>
<s>
Alternatively	O
,	O
the	O
issue	O
of	O
biased	O
predictor	O
selection	O
can	O
be	O
avoided	O
by	O
the	O
Conditional	O
Inference	O
approach	O
,	O
a	O
two-stage	O
approach	O
,	O
or	O
adaptive	O
leave-one-out	O
feature	B-General_Concept
selection	I-General_Concept
.	O
</s>
<s>
Many	O
data	B-Application
mining	I-Application
software	O
packages	O
provide	O
implementations	O
of	O
one	O
or	O
more	O
decision	B-Algorithm
tree	I-Algorithm
algorithms	O
.	O
</s>
<s>
IBM	B-Algorithm
SPSS	I-Algorithm
Modeler	I-Algorithm
,	O
</s>
<s>
RapidMiner	B-Algorithm
,	O
</s>
<s>
Matlab	B-Language
,	O
</s>
<s>
R	B-Language
(	O
an	O
open-source	O
software	O
environment	O
for	O
statistical	O
computing	O
,	O
which	O
includes	O
several	O
CART	O
implementations	O
such	O
as	O
rpart	O
,	O
party	O
and	O
randomForest	O
packages	O
)	O
,	O
</s>
<s>
Weka	B-Language
(	O
a	O
free	O
and	O
open-source	O
data-mining	B-Application
suite	O
,	O
contains	O
many	O
decision	B-Algorithm
tree	I-Algorithm
algorithms	O
)	O
,	O
</s>
<s>
Orange	B-Application
,	O
</s>
<s>
KNIME	B-Language
,	O
</s>
<s>
scikit-learn	B-Application
(	O
a	O
free	O
and	O
open-source	O
machine	O
learning	O
library	O
for	O
the	O
Python	B-Language
programming	I-Language
language	I-Language
)	O
.	O
</s>
<s>
In	O
a	O
decision	B-Algorithm
tree	I-Algorithm
,	O
all	O
paths	O
from	O
the	O
root	O
node	O
to	O
the	O
leaf	B-Data_Structure
node	I-Data_Structure
proceed	O
by	O
way	O
of	O
conjunction	O
,	O
or	O
AND	O
.	O
</s>
<s>
In	O
a	O
decision	B-Algorithm
graph	I-Algorithm
,	O
it	O
is	O
possible	O
to	O
use	O
disjunctions	O
(	O
ORs	O
)	O
to	O
join	O
two	O
more	O
paths	O
together	O
using	O
minimum	O
message	O
length	O
(	O
MML	O
)	O
.	O
</s>
<s>
Decision	B-Algorithm
graphs	I-Algorithm
have	O
been	O
further	O
extended	O
to	O
allow	O
for	O
previously	O
unstated	O
new	O
attributes	O
to	O
be	O
learnt	O
dynamically	O
and	O
used	O
at	O
different	O
places	O
within	O
the	O
graph	O
.	O
</s>
<s>
In	O
general	O
,	O
decision	B-Algorithm
graphs	I-Algorithm
infer	O
models	O
with	O
fewer	O
leaves	B-Data_Structure
than	O
decision	B-Algorithm
trees	I-Algorithm
.	O
</s>
<s>
Evolutionary	O
algorithms	O
have	O
been	O
used	O
to	O
avoid	O
local	O
optimal	O
decisions	O
and	O
search	O
the	O
decision	B-Algorithm
tree	I-Algorithm
space	O
with	O
little	O
a	O
priori	O
bias	O
.	O
</s>
<s>
It	O
is	O
also	O
possible	O
for	O
a	O
tree	O
to	O
be	O
sampled	O
using	O
MCMC	B-General_Concept
.	O
</s>
<s>
Or	O
several	O
trees	B-Algorithm
can	O
be	O
constructed	O
parallelly	O
to	O
reduce	O
the	O
expected	O
number	O
of	O
tests	O
till	O
classification	B-General_Concept
.	O
</s>
