The divergence satisfies three properties, hereafter referred to as the divergence
properties:
1. Self-similarity: hðX; XÞ = 0.
2. Self-identification: hðX; YÞ = 0 only if X ¼ Y.
3. Positively: hðX; YÞ ! 0 for all f ; g.
In this paper, the right value of the confidence interval is introduced as the threshold
value. Confidence interval is an interval centered on the estimated value, which is used
to determine the possible range of the true value according to the estimated value.
Generally, [a, b] is used to represent the interval of the error range of the sample which
could estimate the total mean value, where the specific values of a and b depend on the
credibility of the result that “the area contains the total mean.” The value of confidence
interval lies in its ability to quantify the uncertainty of estimation, which provides a
lower and upper limit and a possibility. As a separate radius measurement, the confidence interval is often referred to as the likelihood and represents estimated uncertainty
by using error maps. In general, the larger the sample is estimated, the more accurate
the estimate and the smaller the confidence interval.
For population X $ Nðl; r
2
Þ, assume that X 1 ; X 2 ; . . .; X n is a sample from X, for
U ¼
XÀl
r=
ffiffi
n
p $ Nð0; 1Þ, the confidence interval of confidence degree 1 À a is
X À
r ffiffi
n
p u a=2 ; X þ
r ffiffi
n
p u a=2
. In general, the larger the sample is estimated, the more
accurate the estimate and the smaller the confidence interval.
2.3 Algorithm Implementation
The first thing to do to achieve the purpose of the paper is to train the restricted
Boltzmann machine. The goal of training is to obtain the maximum likelihood of the
input samples, so that the Gibbs distribution represented by the GRBM network is
closest to the distribution represented by the sample itself. In order to obtain maximum
likelihood, it is necessary to derive the parameters and maximize the logarithmic
likelihood function step by step with the gradient rise method until the stopping
condition is reached. The following likelihood functions should be maximized
L h;S ¼
Y ns
i¼1
Pðv
i
Þ
ð 8Þ
ln L h;S ¼ ln
Y ns
i¼1
Pðv
i
Þ ¼
X ns
i¼1
ln Pðv
i
Þ
ð 9Þ
Data Stream Adaptive Partitioning of Sliding …
223
properties:
1. Self-similarity: hðX; XÞ = 0.
2. Self-identification: hðX; YÞ = 0 only if X ¼ Y.
3. Positively: hðX; YÞ ! 0 for all f ; g.
In this paper, the right value of the confidence interval is introduced as the threshold
value. Confidence interval is an interval centered on the estimated value, which is used
to determine the possible range of the true value according to the estimated value.
Generally, [a, b] is used to represent the interval of the error range of the sample which
could estimate the total mean value, where the specific values of a and b depend on the
credibility of the result that “the area contains the total mean.” The value of confidence
interval lies in its ability to quantify the uncertainty of estimation, which provides a
lower and upper limit and a possibility. As a separate radius measurement, the confidence interval is often referred to as the likelihood and represents estimated uncertainty
by using error maps. In general, the larger the sample is estimated, the more accurate
the estimate and the smaller the confidence interval.
For population X $ Nðl; r
2
Þ, assume that X 1 ; X 2 ; . . .; X n is a sample from X, for
U ¼
XÀl
r=
ffiffi
n
p $ Nð0; 1Þ, the confidence interval of confidence degree 1 À a is
X À
r ffiffi
n
p u a=2 ; X þ
r ffiffi
n
p u a=2
. In general, the larger the sample is estimated, the more
accurate the estimate and the smaller the confidence interval.
2.3 Algorithm Implementation
The first thing to do to achieve the purpose of the paper is to train the restricted
Boltzmann machine. The goal of training is to obtain the maximum likelihood of the
input samples, so that the Gibbs distribution represented by the GRBM network is
closest to the distribution represented by the sample itself. In order to obtain maximum
likelihood, it is necessary to derive the parameters and maximize the logarithmic
likelihood function step by step with the gradient rise method until the stopping
condition is reached. The following likelihood functions should be maximized
L h;S ¼
Y ns
i¼1
Pðv
i
Þ
ð 8Þ
ln L h;S ¼ ln
Y ns
i¼1
Pðv
i
Þ ¼
X ns
i¼1
ln Pðv
i
Þ
ð 9Þ
Data Stream Adaptive Partitioning of Sliding …
223