Details

Given

n

feature vectors of size

p

and a vector of class labels , where describes the class to which the feature vector belongs, and a weak learner algorithm, the problem is to build a two-class BrownBoost classifier.

Calculate , where:
is an inverse error function,
is a target classification error of the algorithm defined as

is the error function,
is a hypothesis formulated by the
i
-th weak learner,
i = 1, ldots, M
,
is the weight of the hypothesis.
Set initial prediction values: .
Set “remaining timing”: .
Do for until
With each feature vector and its label of positive weight, associate .
Call the weak learner with the distribution defined by normalizing Lmath:
W_i(x, y)
to receive a hypothesis .
Solve the differential equation

with given boundary conditions
t = 0
and to find and such that either or , where is a given small constant needed to avoid degenerate cases.
Update the prediction values: .
Update “remaining time”: .
End do

The result of the model training is the array of

M

weak learners .

Given the BrownBoost classifier and

r

feature vectors , the problem is to calculate the final classification confidence, a number from the interval , using the rule:

Batch Processing

Parameter	Default Value	Description
algorithmFPType	float	The floating-point type that the algorithm uses for intermediate computations. Can be float or double .
method	defaultDense	The computation method used by the BrownBoost classifier. The only training method supported so far is the Y. Freund’s method.
nClasses	2	The number of classes.
weakLearnerTraining	DEPRECATED : Pointer to an object of the weak learner training class USE INSTEAD : Pointer to an object of the classification stump training class	DEPRECATED : Pointer to the training algorithm of the weak learner. By default, a stump weak learner is used. USE INSTEAD : Pointer to the classifier training algorithm. Be default, a classification stump with gini split criterion is used.
weakLearnerPrediction	DEPRECATED : Pointer to an object of the weak learner prediction class USE INSTEAD : Pointer to an object of the classification stump prediction class	DEPRECATED : Pointer to the prediction algorithm of the weak learner. By default, a stump weak learner is used. USE INSTEAD : Pointer to the classifier prediction algorithm. Be default, a classification stump with gini split criterion is used.
accuracyThreshold	0.01	BrownBoost training accuracy .
maxIterations	100	The maximal number of iterations for the BrownBoost algorithm.
newtonRaphsonAccuracyThreshold		Accuracy threshold of the Newton-Raphson method used underneath the BrownBoost algorithm.
newtonRaphsonMaxIterations	100	The maximal number of Newton-Raphson iterations in the algorithm.
degenerateCasesThreshold		The threshold used to avoid degenerate cases.

Parameter	Default Value	Description
algorithmFPType	float	The floating-point type that the algorithm uses for intermediate computations. Can be float or double .
method	defaultDense	Performance-oriented computation method, the only method supported by the BrownBoost classifier.
nClasses	2	The number of classes.
weakLearnerPrediction	DEPRECATED : Pointer to an object of the weak learner prediction class USE INSTEAD : Pointer to an object of the classification stump prediction class	DEPRECATED : Pointer to the prediction algorithm of the weak learner. By default, a stump weak learner is used. USE INSTEAD : Pointer to the classifier prediction algorithm. Be default, a classification stump with gini split criterion is used.
accuracyThreshold	0.01	BrownBoost training accuracy .

Examples