1143 words - 5 pages

In this section, we discuss the relation works with MAMEDA.

It composes of two subsections. In subsection A, the

framework of EDA is described, and we have tried to present

a category of the methods are used for estimation the

structures in multivariate EDAs. In subsection B, we review

some of the MAs, EAs and EADs method presented on the

DOPs.

A. EDA

The general steps of EDAs have been used in stationary

optimization problems are as follows [35]:

1) Generate initial populations D with uniform distribution

of variables, and evaluate them.

2) Select N promising individuals from the populationD.

3) Estimate best structure based on the selected individuals.

4) Sampling new individuals based on the parameter

estimated.

5) Evaluate new individuals, and replace old individuals.

6) If a termination criterion is not met, go to step 2.

The above steps usually are used for multivariate EADs. In

univariate EDA, there is not structure learning, and bivariate

EDAs are different in structure learning and sampling steps.

The structure learning is more important part and there are

several works in this field. So, we focus on this step.

We assume each individual in search space has n dimension

or n variables. In the structure learning we must calculate the

following probability, is parents set of variable , if univariate EDAs is used

then ∅. As we described in introduction, the probability

graphical models (PGM) are used for structure representation,

or presentation of the estimated structure. For example, in Fig.

I is represented a structure with four variables that used of

Gaussian model.

Structure learning consists of two components. First, with

attention to the selected individuals, the best structure is

estimated, approximately. Second, the parameters of structure

estimated would be calculated. There are several methods for

structure estimation and many statistical methods for

evaluation the goodness of structures [43], [2] and [16].

In introduction, we discussed three models for represent the

structures. There are many statistical methods to estimate and

evaluate the structures. Some of these methods are utilized in

discrete environments. Some of the structure estimation

methods are similar in Bayesian and Gaussian networks. We

explain some of these methods.

In Gaussian networks, it is considered, each variable of

solutions is continuous and each local density function is the

linear-regression model. One of the methods to generate

Gaussian based models is to use the detecting independencies

between variables [55]. Some of the methods that are based on

this idea are as follow [21]:

1) The likelihood ratio test.

2) The Wald test.

3) The efficient score test.

4) The modified profile likelihood ratio test.

5) The fisher’s statistic.

is one of the algorithms uses likelihood ratio test

for structure learning [21]. Another method which has been

presented to generate models in Gaussian networks is BG

[16], which is a continuous version of

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