Contents

# Details

Given
n
feature vectors
x
1
=(
x
11
,…,
x
1
p
),...,
x
n
=(
x
n
1
,…,
x
np
) of size
p
, a vector of class labels y=(
y
1
,…,
y
n
), where
y
i
K
= {-1, 1} describes the class to which the feature vector
x
i
belongs, and a weak learner algorithm, the problem is to build a two-class BrownBoost classifier.

## Training Stage

The model is trained using the Freund method [ Freund01 ] as follows:
1. Calculate
c
=
erfinv
2
(1 -
ε
), where
erfinv
(
x
) is an inverse error function,
ε
is a target classification error of the algorithm defined as  erf
(
x
) is the error function,
h
i
(
x
) is a hypothesis formulated by the
i
-th weak learner,
i
= 1,...,
M
,
α
i
is the weight of the hypothesis.
2. Set initial prediction values:
r
1
(
x, y
) = 0.
3. Set "remaining timing":
s
1
=
c
.
4. Do for
i
=1,2,... until
s
i
+1
0
1. With each feature vector and its label of positive weight, associate 2. Call the weak learner with the distribution defined by normalizing
W
i
(
x, y
h
i
(
x
)
3. Solve the differential equation with given boundary conditions
t
= 0 and
α
= 0 to find
t
i
=
t
* > 0 and
α
i
=
α
* such that either
γ
ν
or
t
* =
s
i
, where
ν
is a given small constant needed to avoid degenerate cases
4. Update the prediction values:
r
i
+1
(
x, y
) =
r
i
(
x, y
)+
α
i
h
i
(
x
)
y
5. Update "remaining time":
s
i
+1
=
s
i
-
t
i
End do
The result of the model training is the array of
M
weak learners
h
i
.

## Prediction Stage

Given the BrownBoost classifier and
r
feature vectors
x
1
,…,
x
r
, the problem is to calculate the final classification confidence, a number from the interval [-1, 1], using the rule #### Product and Performance Information

1

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Notice revision #20110804