<s>
Supervised	B-General_Concept
learning	I-General_Concept
(	O
SL	O
)	O
is	O
a	O
machine	O
learning	O
paradigm	O
for	O
problems	O
where	O
the	O
available	O
data	O
consists	O
of	O
labeled	O
examples	O
,	O
meaning	O
that	O
each	O
data	O
point	O
contains	O
features	O
(	O
covariates	O
)	O
and	O
an	O
associated	O
label	O
.	O
</s>
<s>
The	O
goal	O
of	O
supervised	B-General_Concept
learning	I-General_Concept
algorithms	O
is	O
learning	O
a	O
function	O
that	O
maps	B-Algorithm
feature	B-Algorithm
vectors	I-Algorithm
(	O
inputs	O
)	O
to	O
labels	O
(	O
output	O
)	O
,	O
based	O
on	O
example	O
input-output	O
pairs	O
.	O
</s>
<s>
In	O
supervised	B-General_Concept
learning	I-General_Concept
,	O
each	O
example	O
is	O
a	O
pair	O
consisting	O
of	O
an	O
input	O
object	O
(	O
typically	O
a	O
vector	O
)	O
and	O
a	O
desired	O
output	O
value	O
(	O
also	O
called	O
the	O
supervisory	O
signal	O
)	O
.	O
</s>
<s>
A	O
supervised	B-General_Concept
learning	I-General_Concept
algorithm	O
analyzes	O
the	O
training	O
data	O
and	O
produces	O
an	O
inferred	O
function	O
,	O
which	O
can	O
be	O
used	O
for	O
mapping	O
new	O
examples	O
.	O
</s>
<s>
This	O
requires	O
the	O
learning	O
algorithm	O
to	O
generalize	O
from	O
the	O
training	O
data	O
to	O
unseen	O
situations	O
in	O
a	O
"	O
reasonable	O
"	O
way	O
(	O
see	O
inductive	B-General_Concept
bias	I-General_Concept
)	O
.	O
</s>
<s>
This	O
statistical	O
quality	O
of	O
an	O
algorithm	O
is	O
measured	O
through	O
the	O
so-called	O
generalization	B-Algorithm
error	I-Algorithm
.	O
</s>
<s>
To	O
solve	O
a	O
given	O
problem	O
of	O
supervised	B-General_Concept
learning	I-General_Concept
,	O
one	O
has	O
to	O
perform	O
the	O
following	O
steps	O
:	O
</s>
<s>
Typically	O
,	O
the	O
input	O
object	O
is	O
transformed	O
into	O
a	O
feature	B-Algorithm
vector	I-Algorithm
,	O
which	O
contains	O
a	O
number	O
of	O
features	O
that	O
are	O
descriptive	O
of	O
the	O
object	O
.	O
</s>
<s>
The	O
number	O
of	O
features	O
should	O
not	O
be	O
too	O
large	O
,	O
because	O
of	O
the	O
curse	B-Algorithm
of	I-Algorithm
dimensionality	I-Algorithm
;	O
but	O
should	O
contain	O
enough	O
information	O
to	O
accurately	O
predict	O
the	O
output	O
.	O
</s>
<s>
For	O
example	O
,	O
the	O
engineer	O
may	O
choose	O
to	O
use	O
support-vector	B-Algorithm
machines	I-Algorithm
or	O
decision	B-Algorithm
trees	I-Algorithm
.	O
</s>
<s>
Some	O
supervised	B-General_Concept
learning	I-General_Concept
algorithms	O
require	O
the	O
user	O
to	O
determine	O
certain	O
control	O
parameters	O
.	O
</s>
<s>
These	O
parameters	O
may	O
be	O
adjusted	O
by	O
optimizing	O
performance	O
on	O
a	O
subset	O
(	O
called	O
a	O
validation	O
set	O
)	O
of	O
the	O
training	O
set	O
,	O
or	O
via	O
cross-validation	B-Application
.	O
</s>
<s>
A	O
wide	O
range	O
of	O
supervised	B-General_Concept
learning	I-General_Concept
algorithms	O
are	O
available	O
,	O
each	O
with	O
its	O
strengths	O
and	O
weaknesses	O
.	O
</s>
<s>
There	O
is	O
no	O
single	O
learning	O
algorithm	O
that	O
works	O
best	O
on	O
all	O
supervised	B-General_Concept
learning	I-General_Concept
problems	O
(	O
see	O
the	O
No	O
free	O
lunch	O
theorem	O
)	O
.	O
</s>
<s>
There	O
are	O
four	O
major	O
issues	O
to	O
consider	O
in	O
supervised	B-General_Concept
learning	I-General_Concept
:	O
</s>
<s>
A	O
key	O
aspect	O
of	O
many	O
supervised	B-General_Concept
learning	I-General_Concept
methods	O
is	O
that	O
they	O
are	O
able	O
to	O
adjust	O
this	O
tradeoff	O
between	O
bias	O
and	O
variance	O
(	O
either	O
automatically	O
or	O
by	O
providing	O
a	O
bias/variance	O
parameter	O
that	O
the	O
user	O
can	O
adjust	O
)	O
.	O
</s>
<s>
If	O
the	O
input	O
feature	B-Algorithm
vectors	I-Algorithm
have	O
large	O
dimensions	O
,	O
learning	O
the	O
function	O
can	O
be	O
difficult	O
even	O
if	O
the	O
true	O
function	O
only	O
depends	O
on	O
a	O
small	O
number	O
of	O
those	O
features	O
.	O
</s>
<s>
In	O
addition	O
,	O
there	O
are	O
many	O
algorithms	O
for	O
feature	B-General_Concept
selection	I-General_Concept
that	O
seek	O
to	O
identify	O
the	O
relevant	O
features	O
and	O
discard	O
the	O
irrelevant	O
ones	O
.	O
</s>
<s>
This	O
is	O
an	O
instance	O
of	O
the	O
more	O
general	O
strategy	O
of	O
dimensionality	B-Algorithm
reduction	I-Algorithm
,	O
which	O
seeks	O
to	O
map	O
the	O
input	O
data	O
into	O
a	O
lower-dimensional	O
space	O
prior	O
to	O
running	O
the	O
supervised	B-General_Concept
learning	I-General_Concept
algorithm	O
.	O
</s>
<s>
Attempting	O
to	O
fit	O
the	O
data	O
too	O
carefully	O
leads	O
to	O
overfitting	B-Error_Name
.	O
</s>
<s>
You	O
can	O
overfit	B-Error_Name
even	O
when	O
there	O
are	O
no	O
measurement	O
errors	O
(	O
stochastic	O
noise	O
)	O
if	O
the	O
function	O
you	O
are	O
trying	O
to	O
learn	O
is	O
too	O
complex	O
for	O
your	O
learning	O
model	O
.	O
</s>
<s>
In	O
practice	O
,	O
there	O
are	O
several	O
approaches	O
to	O
alleviate	O
noise	O
in	O
the	O
output	O
values	O
such	O
as	O
early	B-Algorithm
stopping	I-Algorithm
to	O
prevent	O
overfitting	B-Error_Name
as	O
well	O
as	O
detecting	B-Algorithm
and	O
removing	O
the	O
noisy	O
training	O
examples	O
prior	O
to	O
training	O
the	O
supervised	B-General_Concept
learning	I-General_Concept
algorithm	O
.	O
</s>
<s>
There	O
are	O
several	O
algorithms	O
that	O
identify	O
noisy	O
training	O
examples	O
and	O
removing	O
the	O
suspected	O
noisy	O
training	O
examples	O
prior	O
to	O
training	O
has	O
decreased	O
generalization	B-Algorithm
error	I-Algorithm
with	O
statistical	B-General_Concept
significance	I-General_Concept
.	O
</s>
<s>
If	O
the	O
feature	B-Algorithm
vectors	I-Algorithm
include	O
features	O
of	O
many	O
different	O
kinds	O
(	O
discrete	O
,	O
discrete	O
ordered	O
,	O
counts	O
,	O
continuous	O
values	O
)	O
,	O
some	O
algorithms	O
are	O
easier	O
to	O
apply	O
than	O
others	O
.	O
</s>
<s>
Many	O
algorithms	O
,	O
including	O
support-vector	B-Algorithm
machines	I-Algorithm
,	O
linear	B-General_Concept
regression	I-General_Concept
,	O
logistic	O
regression	O
,	O
neural	B-Architecture
networks	I-Architecture
,	O
and	O
nearest	B-General_Concept
neighbor	I-General_Concept
methods	I-General_Concept
,	O
require	O
that	O
the	O
input	O
features	O
be	O
numerical	O
and	O
scaled	O
to	O
similar	O
ranges	O
(	O
e.g.	O
,	O
to	O
the	O
 [ -1 , 1 ] 	O
interval	O
)	O
.	O
</s>
<s>
Methods	O
that	O
employ	O
a	O
distance	O
function	O
,	O
such	O
as	O
nearest	B-General_Concept
neighbor	I-General_Concept
methods	I-General_Concept
and	O
support-vector	B-Algorithm
machines	I-Algorithm
with	I-Algorithm
Gaussian	I-Algorithm
kernels	I-Algorithm
,	O
are	O
particularly	O
sensitive	O
to	O
this	O
.	O
</s>
<s>
An	O
advantage	O
of	O
decision	B-Algorithm
trees	I-Algorithm
is	O
that	O
they	O
easily	O
handle	O
heterogeneous	O
data	O
.	O
</s>
<s>
If	O
the	O
input	O
features	O
contain	O
redundant	O
information	O
(	O
e.g.	O
,	O
highly	O
correlated	O
features	O
)	O
,	O
some	O
learning	O
algorithms	O
(	O
e.g.	O
,	O
linear	B-General_Concept
regression	I-General_Concept
,	O
logistic	O
regression	O
,	O
and	O
distance	B-General_Concept
based	I-General_Concept
methods	I-General_Concept
)	O
will	O
perform	O
poorly	O
because	O
of	O
numerical	O
instabilities	O
.	O
</s>
<s>
If	O
each	O
of	O
the	O
features	O
makes	O
an	O
independent	O
contribution	O
to	O
the	O
output	O
,	O
then	O
algorithms	O
based	O
on	O
linear	O
functions	O
(	O
e.g.	O
,	O
linear	B-General_Concept
regression	I-General_Concept
,	O
logistic	O
regression	O
,	O
support-vector	B-Algorithm
machines	I-Algorithm
,	O
naive	B-General_Concept
Bayes	I-General_Concept
)	O
and	O
distance	O
functions	O
(	O
e.g.	O
,	O
nearest	B-General_Concept
neighbor	I-General_Concept
methods	I-General_Concept
,	O
support-vector	B-Algorithm
machines	I-Algorithm
with	I-Algorithm
Gaussian	I-Algorithm
kernels	I-Algorithm
)	O
generally	O
perform	O
well	O
.	O
</s>
<s>
However	O
,	O
if	O
there	O
are	O
complex	O
interactions	O
among	O
features	O
,	O
then	O
algorithms	O
such	O
as	O
decision	B-Algorithm
trees	I-Algorithm
and	O
neural	B-Architecture
networks	I-Architecture
work	O
better	O
,	O
because	O
they	O
are	O
specifically	O
designed	O
to	O
discover	O
these	O
interactions	O
.	O
</s>
<s>
When	O
considering	O
a	O
new	O
application	O
,	O
the	O
engineer	O
can	O
compare	O
multiple	O
learning	O
algorithms	O
and	O
experimentally	O
determine	O
which	O
one	O
works	O
best	O
on	O
the	O
problem	O
at	O
hand	O
(	O
see	O
cross	B-Application
validation	I-Application
)	O
.	O
</s>
<s>
Given	O
a	O
set	O
of	O
training	O
examples	O
of	O
the	O
form	O
such	O
that	O
is	O
the	O
feature	B-Algorithm
vector	I-Algorithm
of	O
the	O
-th	O
example	O
and	O
is	O
its	O
label	O
(	O
i.e.	O
,	O
class	O
)	O
,	O
a	O
learning	O
algorithm	O
seeks	O
a	O
function	O
,	O
where	O
is	O
the	O
input	O
space	O
and	O
is	O
the	O
output	O
space	O
.	O
</s>
<s>
For	O
example	O
,	O
naive	B-General_Concept
Bayes	I-General_Concept
and	O
linear	B-General_Concept
discriminant	I-General_Concept
analysis	I-General_Concept
are	O
joint	O
probability	O
models	O
,	O
whereas	O
logistic	O
regression	O
is	O
a	O
conditional	O
probability	O
model	O
.	O
</s>
<s>
There	O
are	O
two	O
basic	O
approaches	O
to	O
choosing	O
or	O
:	O
empirical	B-General_Concept
risk	I-General_Concept
minimization	I-General_Concept
and	O
structural	B-General_Concept
risk	I-General_Concept
minimization	I-General_Concept
.	O
</s>
<s>
Empirical	B-General_Concept
risk	I-General_Concept
minimization	I-General_Concept
seeks	O
the	O
function	O
that	O
best	O
fits	O
the	O
training	O
data	O
.	O
</s>
<s>
Structural	B-General_Concept
risk	I-General_Concept
minimization	I-General_Concept
includes	O
a	O
penalty	O
function	O
that	O
controls	O
the	O
bias/variance	O
tradeoff	O
.	O
</s>
<s>
In	O
empirical	B-General_Concept
risk	I-General_Concept
minimization	I-General_Concept
,	O
the	O
supervised	B-General_Concept
learning	I-General_Concept
algorithm	O
seeks	O
the	O
function	O
that	O
minimizes	O
.	O
</s>
<s>
Hence	O
,	O
a	O
supervised	B-General_Concept
learning	I-General_Concept
algorithm	O
can	O
be	O
constructed	O
by	O
applying	O
an	O
optimization	O
algorithm	O
to	O
find	O
.	O
</s>
<s>
When	O
is	O
a	O
conditional	O
probability	O
distribution	O
and	O
the	O
loss	O
function	O
is	O
the	O
negative	O
log	O
likelihood	O
:	O
,	O
then	O
empirical	B-General_Concept
risk	I-General_Concept
minimization	I-General_Concept
is	O
equivalent	O
to	O
maximum	O
likelihood	O
estimation	O
.	O
</s>
<s>
When	O
contains	O
many	O
candidate	O
functions	O
or	O
the	O
training	O
set	O
is	O
not	O
sufficiently	O
large	O
,	O
empirical	B-General_Concept
risk	I-General_Concept
minimization	I-General_Concept
leads	O
to	O
high	O
variance	O
and	O
poor	O
generalization	O
.	O
</s>
<s>
This	O
is	O
called	O
overfitting	B-Error_Name
.	O
</s>
<s>
Structural	B-General_Concept
risk	I-General_Concept
minimization	I-General_Concept
seeks	O
to	O
prevent	O
overfitting	B-Error_Name
by	O
incorporating	O
a	O
regularization	O
penalty	O
into	O
the	O
optimization	O
.	O
</s>
<s>
When	O
,	O
this	O
gives	O
empirical	B-General_Concept
risk	I-General_Concept
minimization	I-General_Concept
with	O
low	O
bias	O
and	O
high	O
variance	O
.	O
</s>
<s>
The	O
value	O
of	O
can	O
be	O
chosen	O
empirically	O
via	O
cross	B-Application
validation	I-Application
.	O
</s>
<s>
In	O
some	O
cases	O
,	O
the	O
solution	O
can	O
be	O
computed	O
in	O
closed	O
form	O
as	O
in	O
naive	B-General_Concept
Bayes	I-General_Concept
and	O
linear	B-General_Concept
discriminant	I-General_Concept
analysis	I-General_Concept
.	O
</s>
<s>
There	O
are	O
several	O
ways	O
in	O
which	O
the	O
standard	O
supervised	B-General_Concept
learning	I-General_Concept
problem	O
can	O
be	O
generalized	O
:	O
</s>
<s>
Semi-supervised	B-General_Concept
learning	I-General_Concept
:	O
In	O
this	O
setting	O
,	O
the	O
desired	O
output	O
values	O
are	O
provided	O
only	O
for	O
a	O
subset	O
of	O
the	O
training	O
data	O
.	O
</s>
<s>
Weak	B-Architecture
supervision	I-Architecture
:	O
In	O
this	O
setting	O
,	O
noisy	O
,	O
limited	O
,	O
or	O
imprecise	O
sources	O
are	O
used	O
to	O
provide	O
supervision	O
signal	O
for	O
labeling	O
training	O
data	O
.	O
</s>
<s>
Active	B-General_Concept
learning	I-General_Concept
:	O
Instead	O
of	O
assuming	O
that	O
all	O
of	O
the	O
training	O
examples	O
are	O
given	O
at	O
the	O
start	O
,	O
active	B-General_Concept
learning	I-General_Concept
algorithms	O
interactively	O
collect	O
new	O
examples	O
,	O
typically	O
by	O
making	O
queries	B-Library
to	O
a	O
human	O
user	O
.	O
</s>
<s>
Often	O
,	O
the	O
queries	B-Library
are	O
based	O
on	O
unlabeled	O
data	O
,	O
which	O
is	O
a	O
scenario	O
that	O
combines	O
semi-supervised	B-General_Concept
learning	I-General_Concept
with	O
active	B-General_Concept
learning	I-General_Concept
.	O
</s>
<s>
Structured	B-General_Concept
prediction	I-General_Concept
:	O
When	O
the	O
desired	O
output	O
value	O
is	O
a	O
complex	O
object	O
,	O
such	O
as	O
a	O
parse	O
tree	O
or	O
a	O
labeled	O
graph	O
,	O
then	O
standard	O
methods	O
must	O
be	O
extended	O
.	O
</s>
<s>
Minimum	O
message	O
length	O
(	O
decision	B-Algorithm
trees	I-Algorithm
,	O
decision	B-Algorithm
graphs	I-Algorithm
,	O
etc	O
.	O
)	O
</s>
