<s>
BrownBoost	B-Algorithm
is	O
a	O
boosting	B-Algorithm
algorithm	O
that	O
may	O
be	O
robust	O
to	O
noisy	O
datasets	O
.	O
</s>
<s>
BrownBoost	B-Algorithm
is	O
an	O
adaptive	O
version	O
of	O
the	O
boost	O
by	O
majority	O
algorithm	O
.	O
</s>
<s>
As	O
is	O
true	O
for	O
all	O
boosting	B-Algorithm
algorithms	O
,	O
BrownBoost	B-Algorithm
is	O
used	O
in	O
conjunction	O
with	O
other	O
machine	O
learning	O
methods	O
.	O
</s>
<s>
BrownBoost	B-Algorithm
was	O
introduced	O
by	O
Yoav	O
Freund	O
in	O
2001	O
.	O
</s>
<s>
AdaBoost	B-Algorithm
performs	O
well	O
on	O
a	O
variety	O
of	O
datasets	O
;	O
however	O
,	O
it	O
can	O
be	O
shown	O
that	O
AdaBoost	B-Algorithm
does	O
not	O
perform	O
well	O
on	O
noisy	O
data	O
sets	O
.	O
</s>
<s>
This	O
is	O
a	O
result	O
of	O
AdaBoost	B-Algorithm
's	O
focus	O
on	O
examples	O
that	O
are	O
repeatedly	O
misclassified	O
.	O
</s>
<s>
In	O
contrast	O
,	O
BrownBoost	B-Algorithm
effectively	O
"	O
gives	O
up	O
"	O
on	O
examples	O
that	O
are	O
repeatedly	O
misclassified	O
.	O
</s>
<s>
The	O
core	O
assumption	O
of	O
BrownBoost	B-Algorithm
is	O
that	O
noisy	O
examples	O
will	O
be	O
repeatedly	O
mislabeled	O
by	O
the	O
weak	O
hypotheses	O
and	O
non-noisy	O
examples	O
will	O
be	O
correctly	O
labeled	O
frequently	O
enough	O
to	O
not	O
be	O
"	O
given	O
up	O
on.	O
"	O
</s>
<s>
In	O
turn	O
,	O
if	O
the	O
final	O
classifier	O
is	O
learned	O
from	O
the	O
non-noisy	O
examples	O
,	O
the	O
generalization	B-Algorithm
error	I-Algorithm
of	O
the	O
final	O
classifier	O
may	O
be	O
much	O
better	O
than	O
if	O
learned	O
from	O
noisy	O
and	O
non-noisy	O
examples	O
.	O
</s>
<s>
BrownBoost	B-Algorithm
uses	O
a	O
non-convex	O
potential	O
loss	O
function	O
,	O
thus	O
it	O
does	O
not	O
fit	O
into	O
the	O
AdaBoost	B-Algorithm
framework	O
.	O
</s>
<s>
However	O
,	O
in	O
contrast	O
to	O
boosting	B-Algorithm
algorithms	O
that	O
analytically	O
minimize	O
a	O
convex	O
loss	O
function	O
(	O
e.g.	O
</s>
<s>
AdaBoost	B-Algorithm
and	O
LogitBoost	B-Algorithm
)	O
,	O
BrownBoost	B-Algorithm
solves	O
a	O
system	O
of	O
two	O
equations	O
and	O
two	O
unknowns	O
using	O
standard	O
numerical	O
methods	O
.	O
</s>
<s>
The	O
only	O
parameter	O
of	O
BrownBoost	B-Algorithm
(	O
in	O
the	O
algorithm	O
)	O
is	O
the	O
"	O
time	O
"	O
the	O
algorithm	O
runs	O
.	O
</s>
<s>
The	O
theory	O
of	O
BrownBoost	B-Algorithm
states	O
that	O
each	O
hypothesis	O
takes	O
a	O
variable	O
amount	O
of	O
time	O
(	O
in	O
the	O
algorithm	O
)	O
which	O
is	O
directly	O
related	O
to	O
the	O
weight	O
given	O
to	O
the	O
hypothesis	O
.	O
</s>
<s>
The	O
time	O
parameter	O
in	O
BrownBoost	B-Algorithm
is	O
analogous	O
to	O
the	O
number	O
of	O
iterations	O
in	O
AdaBoost	B-Algorithm
.	O
</s>
<s>
A	O
larger	O
value	O
of	O
means	O
that	O
BrownBoost	B-Algorithm
will	O
treat	O
the	O
data	O
as	O
if	O
it	O
were	O
less	O
noisy	O
and	O
therefore	O
will	O
give	O
up	O
on	O
fewer	O
examples	O
.	O
</s>
<s>
Conversely	O
,	O
a	O
smaller	O
value	O
of	O
means	O
that	O
BrownBoost	B-Algorithm
will	O
treat	O
the	O
data	O
as	O
more	O
noisy	O
and	O
give	O
up	O
on	O
more	O
examples	O
.	O
</s>
<s>
time	O
to	O
form	O
the	O
0-1	O
loss	O
function	O
at	O
the	O
end	O
of	O
boosting	B-Algorithm
iterations	O
.	O
</s>
<s>
The	O
final	O
classifier	O
is	O
a	O
linear	O
combination	O
of	O
weak	O
hypotheses	O
and	O
is	O
evaluated	O
in	O
the	O
same	O
manner	O
as	O
most	O
other	O
boosting	B-Algorithm
algorithms	O
.	O
</s>
<s>
In	O
preliminary	O
experimental	O
results	O
with	O
noisy	O
datasets	O
,	O
BrownBoost	B-Algorithm
outperformed	O
AdaBoost	B-Algorithm
's	O
generalization	B-Algorithm
error	I-Algorithm
;	O
however	O
,	O
LogitBoost	B-Algorithm
performed	O
as	O
well	O
as	O
BrownBoost	B-Algorithm
.	O
</s>
<s>
An	O
implementation	O
of	O
BrownBoost	B-Algorithm
can	O
be	O
found	O
in	O
the	O
open	O
source	O
software	O
.	O
</s>
