<s>
A	O
decision	B-Application
tree	I-Application
is	O
a	O
decision	B-Application
support	I-Application
hierarchical	O
model	O
that	O
uses	O
a	O
tree-like	O
model	O
of	O
decisions	O
and	O
their	O
possible	O
consequences	O
,	O
including	O
chance	O
event	O
outcomes	O
,	O
resource	O
costs	O
,	O
and	O
utility	O
.	O
</s>
<s>
Decision	B-Application
trees	I-Application
are	O
commonly	O
used	O
in	O
operations	O
research	O
,	O
specifically	O
in	O
decision	O
analysis	O
,	O
to	O
help	O
identify	O
a	O
strategy	O
most	O
likely	O
to	O
reach	O
a	O
goal	O
,	O
but	O
are	O
also	O
a	O
popular	O
tool	O
in	O
machine	B-Algorithm
learning	I-Algorithm
.	O
</s>
<s>
A	O
decision	B-Application
tree	I-Application
is	O
a	O
flowchart-like	O
structure	O
in	O
which	O
each	O
internal	O
node	O
represents	O
a	O
"	O
test	O
"	O
on	O
an	O
attribute	O
(	O
e.g.	O
</s>
<s>
In	O
decision	O
analysis	O
,	O
a	O
decision	B-Application
tree	I-Application
and	O
the	O
closely	O
related	O
influence	O
diagram	O
are	O
used	O
as	O
a	O
visual	O
and	O
analytical	O
decision	B-Application
support	I-Application
tool	O
,	O
where	O
the	O
expected	O
values	O
(	O
or	O
expected	O
utility	O
)	O
of	O
competing	O
alternatives	O
are	O
calculated	O
.	O
</s>
<s>
A	O
decision	B-Application
tree	I-Application
consists	O
of	O
three	O
types	O
of	O
nodes	O
:	O
</s>
<s>
Decision	B-Application
trees	I-Application
are	O
commonly	O
used	O
in	O
operations	O
research	O
and	O
operations	O
management	O
.	O
</s>
<s>
If	O
,	O
in	O
practice	O
,	O
decisions	O
have	O
to	O
be	O
taken	O
online	O
with	O
no	O
recall	O
under	O
incomplete	O
knowledge	O
,	O
a	O
decision	B-Application
tree	I-Application
should	O
be	O
paralleled	O
by	O
a	O
probability	O
model	O
as	O
a	O
best	O
choice	O
model	O
or	O
online	O
selection	O
model	O
algorithm	O
.	O
</s>
<s>
Another	O
use	O
of	O
decision	B-Application
trees	I-Application
is	O
as	O
a	O
descriptive	O
means	O
for	O
calculating	O
conditional	O
probabilities	O
.	O
</s>
<s>
Decision	B-Application
trees	I-Application
,	O
influence	O
diagrams	O
,	O
utility	O
functions	O
,	O
and	O
other	O
decision	O
analysis	O
tools	O
and	O
methods	O
are	O
taught	O
to	O
undergraduate	O
students	O
in	O
schools	O
of	O
business	O
,	O
health	O
economics	O
,	O
and	O
public	O
health	O
,	O
and	O
are	O
examples	O
of	O
operations	O
research	O
or	O
management	O
science	O
methods	O
.	O
</s>
<s>
Drawn	O
from	O
left	O
to	O
right	O
,	O
a	O
decision	B-Application
tree	I-Application
has	O
only	O
burst	O
nodes	O
(	O
splitting	O
paths	O
)	O
but	O
no	O
sink	O
nodes	O
(	O
converging	O
paths	O
)	O
.	O
</s>
<s>
Traditionally	O
,	O
decision	B-Application
trees	I-Application
have	O
been	O
created	O
manually	O
–	O
as	O
the	O
aside	O
example	O
shows	O
–	O
although	O
increasingly	O
,	O
specialized	O
software	O
is	O
employed	O
.	O
</s>
<s>
The	O
decision	B-Application
tree	I-Application
can	O
be	O
linearized	O
into	O
decision	O
rules	O
,	O
where	O
the	O
outcome	O
is	O
the	O
contents	O
of	O
the	O
leaf	O
node	O
,	O
and	O
the	O
conditions	O
along	O
the	O
path	O
form	O
a	O
conjunction	O
in	O
the	O
if	O
clause	O
.	O
</s>
<s>
Decision	O
rules	O
can	O
be	O
generated	O
by	O
constructing	O
association	B-Algorithm
rules	I-Algorithm
with	O
the	O
target	O
variable	O
on	O
the	O
right	O
.	O
</s>
<s>
Commonly	O
a	O
decision	B-Application
tree	I-Application
is	O
drawn	O
using	O
flowchart	B-Language
symbols	O
as	O
it	O
is	O
easier	O
for	O
many	O
to	O
read	O
and	O
understand	O
.	O
</s>
<s>
In	O
this	O
example	O
,	O
a	O
decision	B-Application
tree	I-Application
can	O
be	O
drawn	O
to	O
illustrate	O
the	O
principles	O
of	O
diminishing	O
returns	O
on	O
beach	O
#1	O
.	O
</s>
<s>
The	O
decision	B-Application
tree	I-Application
illustrates	O
that	O
when	O
sequentially	O
distributing	O
lifeguards	O
,	O
placing	O
a	O
first	O
lifeguard	O
on	O
beach	O
#1	O
would	O
be	O
optimal	O
if	O
there	O
is	O
only	O
the	O
budget	O
for	O
1	O
lifeguard	O
.	O
</s>
<s>
Much	O
of	O
the	O
information	O
in	O
a	O
decision	B-Application
tree	I-Application
can	O
be	O
represented	O
more	O
compactly	O
as	O
an	O
influence	O
diagram	O
,	O
focusing	O
attention	O
on	O
the	O
issues	O
and	O
relationships	O
between	O
events	O
.	O
</s>
<s>
Decision	B-Application
trees	I-Application
can	O
also	O
be	O
seen	O
as	O
generative	O
models	O
of	O
induction	O
rules	O
from	O
empirical	O
data	O
.	O
</s>
<s>
An	O
optimal	O
decision	B-Application
tree	I-Application
is	O
then	O
defined	O
as	O
a	O
tree	O
that	O
accounts	O
for	O
most	O
of	O
the	O
data	O
,	O
while	O
minimizing	O
the	O
number	O
of	O
levels	O
(	O
or	O
"	O
questions	O
"	O
)	O
.	O
</s>
<s>
Several	O
algorithms	O
to	O
generate	O
such	O
optimal	O
trees	O
have	O
been	O
devised	O
,	O
such	O
as	O
ID3/4/5	O
,	O
CLS	O
,	O
ASSISTANT	O
,	O
and	O
CART	O
.	O
</s>
<s>
Among	O
decision	B-Application
support	I-Application
tools	O
,	O
decision	B-Application
trees	I-Application
(	O
and	O
influence	O
diagrams	O
)	O
have	O
several	O
advantages	O
.	O
</s>
<s>
Decision	B-Application
trees	I-Application
:	O
</s>
<s>
People	O
are	O
able	O
to	O
understand	O
decision	B-Application
tree	I-Application
models	I-Application
after	O
a	O
brief	O
explanation	O
.	O
</s>
<s>
Use	O
a	O
white	B-General_Concept
box	I-General_Concept
model	O
.	O
</s>
<s>
Disadvantages	O
of	O
decision	B-Application
trees	I-Application
:	O
</s>
<s>
They	O
are	O
unstable	O
,	O
meaning	O
that	O
a	O
small	O
change	O
in	O
the	O
data	O
can	O
lead	O
to	O
a	O
large	O
change	O
in	O
the	O
structure	O
of	O
the	O
optimal	O
decision	B-Application
tree	I-Application
.	O
</s>
<s>
This	O
can	O
be	O
remedied	O
by	O
replacing	O
a	O
single	O
decision	B-Application
tree	I-Application
with	O
a	O
random	B-Algorithm
forest	I-Algorithm
of	O
decision	B-Application
trees	I-Application
,	O
but	O
a	O
random	B-Algorithm
forest	I-Algorithm
is	O
not	O
as	O
easy	O
to	O
interpret	O
as	O
a	O
single	O
decision	B-Application
tree	I-Application
.	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
those	O
attributes	O
with	O
more	O
levels	O
.	O
</s>
<s>
A	O
few	O
things	O
should	O
be	O
considered	O
when	O
improving	O
the	O
accuracy	O
of	O
the	O
decision	B-Application
tree	I-Application
classifier	O
.	O
</s>
<s>
The	O
following	O
are	O
some	O
possible	O
optimizations	O
to	O
consider	O
when	O
looking	O
to	O
make	O
sure	O
the	O
decision	B-Application
tree	I-Application
model	I-Application
produced	O
makes	O
the	O
correct	O
decision	O
or	O
classification	O
.	O
</s>
<s>
The	O
accuracy	O
of	O
the	O
decision	B-Application
tree	I-Application
can	O
change	O
based	O
on	O
the	O
depth	O
of	O
the	O
decision	B-Application
tree	I-Application
.	O
</s>
<s>
It	O
is	O
important	O
to	O
note	O
that	O
a	O
deeper	O
tree	O
is	O
not	O
always	O
better	O
when	O
optimizing	O
the	O
decision	B-Application
tree	I-Application
.	O
</s>
<s>
There	O
is	O
also	O
the	O
possibility	O
that	O
the	O
actual	O
algorithm	O
building	O
the	O
decision	B-Application
tree	I-Application
will	O
get	O
significantly	O
slower	O
as	O
the	O
tree	O
gets	O
deeper	O
.	O
</s>
<s>
Occasionally	O
,	O
going	O
deeper	O
in	O
the	O
tree	O
can	O
cause	O
an	O
accuracy	O
decrease	O
in	O
general	O
,	O
so	O
it	O
is	O
very	O
important	O
to	O
test	O
modifying	O
the	O
depth	O
of	O
the	O
decision	B-Application
tree	I-Application
and	O
selecting	O
the	O
depth	O
that	O
produces	O
the	O
best	O
results	O
.	O
</s>
<s>
Accuracy	O
of	O
the	O
decision-tree	B-Algorithm
classification	O
model	O
increases	O
.	O
</s>
<s>
The	O
node	O
splitting	O
function	O
used	O
can	O
have	O
an	O
impact	O
on	O
improving	O
the	O
accuracy	O
of	O
the	O
decision	B-Application
tree	I-Application
.	O
</s>
<s>
For	O
example	O
,	O
using	O
the	O
information-gain	B-Algorithm
function	O
may	O
yield	O
better	O
results	O
than	O
using	O
the	O
phi	O
function	O
.	O
</s>
<s>
The	O
phi	O
function	O
is	O
known	O
as	O
a	O
measure	O
of	O
“	O
goodness	O
”	O
of	O
a	O
candidate	O
split	O
at	O
a	O
node	O
in	O
the	O
decision	B-Application
tree	I-Application
.	O
</s>
<s>
The	O
information	B-Algorithm
gain	I-Algorithm
function	O
is	O
known	O
as	O
a	O
measure	O
of	O
the	O
“	O
reduction	O
in	O
entropy	O
”	O
.	O
</s>
<s>
In	O
the	O
following	O
,	O
we	O
will	O
build	O
two	O
decision	B-Application
trees	I-Application
.	O
</s>
<s>
One	O
decision	B-Application
tree	I-Application
will	O
be	O
built	O
using	O
the	O
phi	O
function	O
to	O
split	O
the	O
nodes	O
and	O
one	O
decision	B-Application
tree	I-Application
will	O
be	O
built	O
using	O
the	O
information	B-Algorithm
gain	I-Algorithm
function	O
to	O
split	O
the	O
nodes	O
.	O
</s>
<s>
One	O
major	O
drawback	O
of	O
information	B-Algorithm
gain	I-Algorithm
is	O
that	O
the	O
feature	O
that	O
is	O
chosen	O
as	O
the	O
next	O
node	O
in	O
the	O
tree	O
tends	O
to	O
have	O
more	O
unique	O
values	O
.	O
</s>
<s>
An	O
advantage	O
of	O
information	B-Algorithm
gain	I-Algorithm
is	O
that	O
it	O
tends	O
to	O
choose	O
the	O
most	O
impactful	O
features	O
that	O
are	O
close	O
to	O
the	O
root	O
of	O
the	O
tree	O
.	O
</s>
<s>
This	O
is	O
the	O
information	B-Algorithm
gain	I-Algorithm
function	O
formula	O
.	O
</s>
<s>
The	O
formula	O
states	O
the	O
information	B-Algorithm
gain	I-Algorithm
is	O
a	O
function	O
of	O
the	O
entropy	O
of	O
a	O
node	O
of	O
the	O
decision	B-Application
tree	I-Application
minus	O
the	O
entropy	O
of	O
a	O
candidate	O
split	O
at	O
node	O
t	O
of	O
a	O
decision	B-Application
tree	I-Application
.	O
</s>
<s>
We	O
will	O
set	O
D	O
,	O
which	O
is	O
the	O
depth	O
of	O
the	O
decision	B-Application
tree	I-Application
we	O
are	O
building	O
,	O
to	O
three	O
(	O
D	O
=	O
3	O
)	O
.	O
</s>
<s>
Now	O
,	O
we	O
can	O
use	O
the	O
formulas	O
to	O
calculate	O
the	O
phi	O
function	O
values	O
and	O
information	B-Algorithm
gain	I-Algorithm
values	O
for	O
each	O
M	O
in	O
the	O
dataset	O
.	O
</s>
<s>
In	O
information	B-Algorithm
gain	I-Algorithm
and	O
the	O
phi	O
function	O
we	O
consider	O
the	O
optimal	O
split	O
to	O
be	O
the	O
mutation	O
that	O
produces	O
the	O
highest	O
value	O
for	O
information	B-Algorithm
gain	I-Algorithm
or	O
the	O
phi	O
function	O
.	O
</s>
<s>
Now	O
assume	O
that	O
M1	O
has	O
the	O
highest	O
phi	O
function	O
value	O
and	O
M4	O
has	O
the	O
highest	O
information	B-Algorithm
gain	I-Algorithm
value	O
.	O
</s>
<s>
The	O
M1	O
mutation	O
will	O
be	O
the	O
root	O
of	O
our	O
phi	O
function	O
tree	O
and	O
M4	O
will	O
be	O
the	O
root	O
of	O
our	O
information	B-Algorithm
gain	I-Algorithm
tree	O
.	O
</s>
<s>
Disregarding	O
the	O
mutation	O
chosen	O
for	O
the	O
root	O
node	O
,	O
proceed	O
to	O
place	O
the	O
next	O
best	O
features	O
that	O
have	O
the	O
highest	O
values	O
for	O
information	B-Algorithm
gain	I-Algorithm
or	O
the	O
phi	O
function	O
in	O
the	O
left	O
or	O
right	O
child	O
nodes	O
of	O
the	O
decision	B-Application
tree	I-Application
.	O
</s>
<s>
The	O
left	O
tree	O
is	O
the	O
decision	B-Application
tree	I-Application
we	O
obtain	O
from	O
using	O
information	B-Algorithm
gain	I-Algorithm
to	O
split	O
the	O
nodes	O
and	O
the	O
right	O
tree	O
is	O
what	O
we	O
obtain	O
from	O
using	O
the	O
phi	O
function	O
to	O
split	O
the	O
nodes	O
.	O
</s>
<s>
Now	O
assume	O
the	O
classification	O
results	O
from	O
both	O
trees	O
are	O
given	O
using	O
a	O
confusion	B-General_Concept
matrix	I-General_Concept
.	O
</s>
<s>
Information	B-Algorithm
gain	I-Algorithm
confusion	B-General_Concept
matrix	I-General_Concept
:	O
</s>
<s>
Phi	O
function	O
confusion	B-General_Concept
matrix	I-General_Concept
:	O
</s>
<s>
The	O
tree	O
using	O
information	B-Algorithm
gain	I-Algorithm
has	O
the	O
same	O
results	O
when	O
using	O
the	O
phi	O
function	O
when	O
calculating	O
the	O
accuracy	O
.	O
</s>
<s>
When	O
we	O
classify	O
the	O
samples	O
based	O
on	O
the	O
model	O
using	O
information	B-Algorithm
gain	I-Algorithm
we	O
get	O
one	O
true	O
positive	O
,	O
one	O
false	O
positive	O
,	O
zero	O
false	O
negatives	O
,	O
and	O
four	O
true	O
negatives	O
.	O
</s>
<s>
The	O
next	O
step	O
is	O
to	O
evaluate	O
the	O
effectiveness	O
of	O
the	O
decision	B-Application
tree	I-Application
using	O
some	O
key	O
metrics	O
that	O
will	O
be	O
discussed	O
in	O
the	O
evaluating	O
a	O
decision	B-Application
tree	I-Application
section	O
below	O
.	O
</s>
<s>
The	O
metrics	O
that	O
will	O
be	O
discussed	O
below	O
can	O
help	O
determine	O
the	O
next	O
steps	O
to	O
be	O
taken	O
when	O
optimizing	O
the	O
decision	B-Application
tree	I-Application
.	O
</s>
<s>
The	O
above	O
information	O
is	O
not	O
where	O
it	O
ends	O
for	O
building	O
and	O
optimizing	O
a	O
decision	B-Application
tree	I-Application
.	O
</s>
<s>
There	O
are	O
many	O
techniques	O
for	O
improving	O
the	O
decision	B-Application
tree	I-Application
classification	O
models	O
we	O
build	O
.	O
</s>
<s>
One	O
of	O
the	O
techniques	O
is	O
making	O
our	O
decision	B-Application
tree	I-Application
model	I-Application
from	O
a	O
bootstrapped	B-Application
dataset	O
.	O
</s>
<s>
The	O
bootstrapped	B-Application
dataset	O
helps	O
remove	O
the	O
bias	O
that	O
occurs	O
when	O
building	O
a	O
decision	B-Application
tree	I-Application
model	I-Application
with	O
the	O
same	O
data	O
the	O
model	O
is	O
tested	O
with	O
.	O
</s>
<s>
The	O
ability	O
to	O
leverage	O
the	O
power	O
of	O
random	B-Algorithm
forests	I-Algorithm
can	O
also	O
help	O
significantly	O
improve	O
the	O
overall	O
accuracy	O
of	O
the	O
model	O
being	O
built	O
.	O
</s>
<s>
This	O
method	O
generates	O
many	O
decisions	O
from	O
many	O
decision	B-Application
trees	I-Application
and	O
tallies	O
up	O
the	O
votes	O
from	O
each	O
decision	B-Application
tree	I-Application
to	O
make	O
the	O
final	O
classification	O
.	O
</s>
<s>
There	O
are	O
many	O
techniques	O
,	O
but	O
the	O
main	O
objective	O
is	O
to	O
test	O
building	O
your	O
decision	B-Application
tree	I-Application
model	I-Application
in	O
different	O
ways	O
to	O
make	O
sure	O
it	O
reaches	O
the	O
highest	O
performance	O
level	O
possible	O
.	O
</s>
<s>
It	O
is	O
important	O
to	O
know	O
the	O
measurements	O
used	O
to	O
evaluate	O
decision	B-Application
trees	I-Application
.	O
</s>
<s>
The	O
main	O
metrics	O
used	O
are	O
accuracy	O
,	O
sensitivity	O
,	O
specificity	O
,	O
precision	O
,	O
miss	O
rate	O
,	O
false	B-General_Concept
discovery	I-General_Concept
rate	I-General_Concept
,	O
and	O
false	O
omission	O
rate	O
.	O
</s>
<s>
All	O
these	O
measurements	O
are	O
derived	O
from	O
the	O
number	O
of	O
true	O
positives	O
,	O
false	O
positives	O
,	O
True	O
negatives	O
,	O
and	O
false	O
negatives	O
obtained	O
when	O
running	O
a	O
set	O
of	O
samples	O
through	O
the	O
decision	B-Application
tree	I-Application
classification	O
model	O
.	O
</s>
<s>
Also	O
,	O
a	O
confusion	B-General_Concept
matrix	I-General_Concept
can	O
be	O
made	O
to	O
display	O
these	O
results	O
.	O
</s>
<s>
All	O
these	O
main	O
metrics	O
tell	O
something	O
different	O
about	O
the	O
strengths	O
and	O
weaknesses	O
of	O
the	O
classification	O
model	O
built	O
based	O
on	O
your	O
decision	B-Application
tree	I-Application
.	O
</s>
<s>
For	O
example	O
,	O
A	O
low	O
sensitivity	O
with	O
high	O
specificity	O
could	O
indicate	O
the	O
classification	O
model	O
built	O
from	O
the	O
decision	B-Application
tree	I-Application
does	O
not	O
do	O
well	O
identifying	O
cancer	O
samples	O
over	O
non-cancer	O
samples	O
.	O
</s>
<s>
Let	O
us	O
take	O
the	O
confusion	B-General_Concept
matrix	I-General_Concept
below	O
.	O
</s>
<s>
The	O
confusion	B-General_Concept
matrix	I-General_Concept
shows	O
us	O
the	O
decision	B-Application
tree	I-Application
model	I-Application
classifier	O
built	O
gave	O
11	O
true	O
positives	O
,	O
1	O
false	O
positive	O
,	O
45	O
false	O
negatives	O
,	O
and	O
105	O
true	O
negatives	O
.	O
</s>
<s>
We	O
will	O
now	O
calculate	O
the	O
values	O
accuracy	O
,	O
sensitivity	O
,	O
specificity	O
,	O
precision	O
,	O
miss	O
rate	O
,	O
false	B-General_Concept
discovery	I-General_Concept
rate	I-General_Concept
,	O
and	O
false	O
omission	O
rate	O
.	O
</s>
<s>
False	B-General_Concept
discovery	I-General_Concept
rate	I-General_Concept
(	O
FDR	O
)	O
:	O
</s>
<s>
Once	O
we	O
have	O
calculated	O
the	O
key	O
metrics	O
we	O
can	O
make	O
some	O
initial	O
conclusions	O
on	O
the	O
performance	O
of	O
the	O
decision	B-Application
tree	I-Application
model	I-Application
built	O
.	O
</s>
<s>
These	O
are	O
just	O
a	O
few	O
examples	O
on	O
how	O
to	O
use	O
these	O
values	O
and	O
the	O
meanings	O
behind	O
them	O
to	O
evaluate	O
the	O
decision	B-Application
tree	I-Application
model	I-Application
and	O
improve	O
upon	O
the	O
next	O
iteration	O
.	O
</s>
