Getting Started Guide

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
      ) to receive a hypothesis
      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

Intel's compilers may or may not optimize to the same degree for non-Intel microprocessors for optimizations that are not unique to Intel microprocessors. These optimizations include SSE2, SSE3, and SSSE3 instruction sets and other optimizations. Intel does not guarantee the availability, functionality, or effectiveness of any optimization on microprocessors not manufactured by Intel. Microprocessor-dependent optimizations in this product are intended for use with Intel microprocessors. Certain optimizations not specific to Intel microarchitecture are reserved for Intel microprocessors. Please refer to the applicable product User and Reference Guides for more information regarding the specific instruction sets covered by this notice.

Notice revision #20110804