文件名称:
Attribute Weighting for Averaged One-Dependence Estimators
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文件大小: 373kb
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上传时间: 2019-02-23
详细说明：这是我写的一个论文，关于朴素贝叶斯分类器经过属性权重调整提升分类性能并提出了新算法，名字是WAODE，摘要如下：
Averaged One-Dependence Estimators (AODE) is one of supervised learning algorithm, which relaxes the conditional independent assumption that working on the standard naive Bayes learner. The AODE has shown the reasonable improvement of classifistructures of bn
However, aode does not consider the relationships bet ween the attribute
(super-parent node) which is called one-dependence attribute in AODE with
other normal attributes. We belief that for any pairs of features Ai, A
which have the more dependency to each other, the more confidences for
the probabilistic estimation value of P(A; Ai or P(AiAi we have. Hence
we propose an algorithm based on aode-framework, expect to improve the
performance of aode by considering the relations of features in the real-
world data sets. Base on our work. expert experiences also can be work via
tuning those parameters which reflecting the relationships among the pairs
of attributes in our algorithm
Zheng and Webb(2006) proposed improving AODE method called lazy
elimination for AODE (Simply, LE). LE is an interesting method which is
simple, efficient but can be applied to any Bayesian classifier. LE has de
fined the specialization-gemeralization relationship upon pairwise attributes
and points out that deleting all generalization-attribute-values before train-
ing an classifier can relatively improve the performance of Bayesian classifi-
er.Zheng and Webb(2006) proved that there is no any information lose in
the prediction after deleting the generalization-attribute-values in data set
However, keeping the generalization-attribute-values(useless data) in train-
ing data sets can cause prediction bias under the independence assumption
because independence assumption has the bias per se(violated in real world
problems usually)
Jiang and Zhang(2006) proposed an algorithm named weightily averaged
one-dependence estimators which assigns the weights to super-parent nodes
according the relationships between the super-parent node and class. The
method proposed by (Jiang and Zhang 2006) is different with our proposed
method since that the weight-values in our paper indicate the relationships
between super-parent node with another normal attributes given the class
Jiang et al. (2009) proposed an algorithm called hidden naive Bayes(IIn
B) which is a structure extending method of naive Bayes. In HNB, each
feature in data sets has one hidden parent which is a mixture of the weighted
influences from all other attributes. hNB and our proposed algorithm apply
the same attribute weighting method to measure the relationship between
a pair of attributes by conditional mutual information metric. Both hnB
and WAODE avoid learning structure of bn also. However, our proposed
algorithm WAOdE is different with HNB in two points: the first one is
that the probability estimator of all attribute relies on the hidden parent of
3
Figure 1: An example of naive Bayes learner. Y is class attribute; A, is the i-th attribute
in a data set
A)(
Figure 2: An example of AODE
Figure 3: An example of TaN. y is class attribute; Ai is the i-th attribute in a data set
4
H
Figure 4: An example of hnB. Y is class attribute; Ai is the i-th attribute in a data set
and H:(dash line) presents a hidden parent node of A
that attribute, but in our algorithm Waode the probability estimator of
an attribute depends on the training data sampling. Actually, this kind of
difference stems from the bns structure difference between the hnb and
AODE. The second point, attribute weighing form is difference: the weight
is as a multiplicator in hnb learner, but as a exponent in our WAOde
Contributions of this paper are two-fold
We briefly make a survey of ways to improve AOde
We propose a novel attribute weighting for AOde called Weighted Av-
eraged One-Dependence estimators, simply WAOdE. The WaOde not
only keeps the advantage of AODE, but also considers the dependen-
cy among the attributes by conditional mutual information measure
methods
Our experimental results show that WAODE learning algorithm has a
better improvement compared to standard AODE
The rest of the paper is organized as follows: we briefly discuss AODE
and attribute weighting forms in Section 2. In Section 3, weighted AODE is
proposed. In Section 4, we describe the experiments and results in details
Lastly, we draw conclusions for our study and describe the future work in
the Section 5
A
A
A
A
A
AB
(a) An cxamplc of naive Baycs lcarncr. Y
(b) An cxamplc of AODE.
s class attribute: Ai is the i-th attribute
data set
y
A
A
Ab
A
A
A
A
A
6
(c An cxamplc of TAN. Y is class at-( d)An cxamplc of HNB. Y is class at
tribute: Ai is the i-th attribute in a data tribute: a is the i-th attribute in a data
set
set and H:(dash line) presents a hidden
parent node of A i
Figure 5: The Bayesian net structures of naive Bayes, AODE, TAN and HNB
2. AODE and attribute Weighting Forms
In this section, we give a brief review of AODE. AOdE is a super
vised learning algorithm based on naive Bayes learner, which expends the
naive Bayes Learner by limited relaxing the conditional independent assump-
tion. Averaged one-attribute-dependence is the main feature of AODE. Since
AODE expending from naive Bayes learner. we have to simply introduce the
naive bayes learner first. At last in this section, we discuss the forms of
attribute weighting
2.1. Naive Bayes Classifier
In supervised learning, consider a training data setd=x
composed of n instances, where each instance x=(al,., m) d(in-
dimensional vector)is labeled with class label y E Y. For the posterior
probability of y given x, we have
ply x)=
∝xp(xy)
)(X)
But likelihood, p(xg) cannot be directly estimated from D because of
insufficient data in practice. Naive Bayes uses attributes independence as
sumption to alleviate this problem, from the assumption, p(xy) is shown as
OWS
m
p(xlg)=p(c1,., mIg)p(caly
i=1
Then, the classifier of naive Bayes is shown as follows
maxp(v)llp(cal)
讠=1
2.2. AODE
AOdE structurally expends the naive bayes by averaged one-attribute
dependence method. AODE learning algorithm relies on those test instances
The details of aode is described as follows
Given a test instance x=(a1,., i,..., am, we have p(, x)=p(ylxplx
then
0(3, x) p(gp(xy
X
p(x)
assume that there is a training data set with sufficient data. a test instance
X Should be included in that training data set. Since t i in x, thus
(g,x)=p(x, i,y)=p(y, cip(xg, i
equation 5 combines with the equation 4
p/(y|x)=
p(y, Tip(x)
p(x)
(6
AODE learning algorithm uses equation 6 and bases on attribute indepen
dence assumption, thus we have
m
p(x,)≈1x,x)
where both aj and i are the attribute-values in the test sample x. Hence,
the classifier of aode can be described as follows:
m
arg max
∑v,x)
iy, i
i:1
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