# Bayesian Network Construction

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A Bayesian Network (BN) is a probabilistic graphical model that represents dependencies among variables using nodes and arrows. It helps in utilizing probabilities in Artificial Intelligence. The network can be used to infer unobserved variables, learn parameters, and structure learning. Construction of BN involves understanding variables, values, and relationships among them, as well as quantification of conditional probabilities. Additionally, the Markov Property is considered while forming the network.

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Bayesian Network helps utilize the probabilities in the Artificial Intelligence. It is a form of

probabilistic graphical model. The model shows the dependencies among the variables. One

of the examples of the model can be the representation of diseases and the symptoms. If the

symptoms are available with the individual then the individual can use the tool to understand

the likeliness of various diseases. The representation of the network is through arrows and

nodes. The nodes present in the model denote the quantities that can be identified by the

observers. In some cases, there are variables that are not known completely but can be

inferred from the situation. Such variables are called latent variables, which are also used as

the nodes (Jensen, 1996). Moreover, there are hypothetical variables defined by the

individuals to understand the situations that are also denoted on the nodes of the models. The

diagram given below shows the simple model of the network consisting of nodes and the

dependencies shown through arrows:

The variables shown through the nodes are represented as X = X1+X2+…Xn and the arcs that

are shown in the diagram above is represented by Xi → Xj. The arcs shows the direct

dependencies among the variables they are connected. One of the important aspects that are

used in this network is the conditional probability. The conditional probability shows the

strengths of the dependencies. However, one thing that should be kept in consideration while

forming the nodes and arcs is that the directed cycles should not there (Nielsen 7 Jensen,

probabilistic graphical model. The model shows the dependencies among the variables. One

of the examples of the model can be the representation of diseases and the symptoms. If the

symptoms are available with the individual then the individual can use the tool to understand

the likeliness of various diseases. The representation of the network is through arrows and

nodes. The nodes present in the model denote the quantities that can be identified by the

observers. In some cases, there are variables that are not known completely but can be

inferred from the situation. Such variables are called latent variables, which are also used as

the nodes (Jensen, 1996). Moreover, there are hypothetical variables defined by the

individuals to understand the situations that are also denoted on the nodes of the models. The

diagram given below shows the simple model of the network consisting of nodes and the

dependencies shown through arrows:

The variables shown through the nodes are represented as X = X1+X2+…Xn and the arcs that

are shown in the diagram above is represented by Xi → Xj. The arcs shows the direct

dependencies among the variables they are connected. One of the important aspects that are

used in this network is the conditional probability. The conditional probability shows the

strengths of the dependencies. However, one thing that should be kept in consideration while

forming the nodes and arcs is that the directed cycles should not there (Nielsen 7 Jensen,

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2009 ). If an individual wants to return to a node by moving through the directed arcs, then it

would not reach feasible solution.

As per the inference is concerned, there are three of these within BN. They are given below:

Inferring unobserved variables

Due to the presence of all the observed variables in the Bayesian Network, it becomes easier

to infer the variables that are unobserved. Answering the queries with the help of probability

becomes easier (Murphy, 2002).

Parameter learning

Parameters are used to show the likelihood of one cause over another. The parameters are

generally unknown and require estimation.

Structure learning

The structures are defined in BNs with the help of experts and then inferences are derived.

Data are used to form the structure as in most cases it becomes challenging due to its

complexity.

The construction of Bayesian Networ requires understanding few steps. These steps are given

below:

Nodes and values

This is the first step where the individual tries to understand the variables that are into play.

There are some questions that are considered while selecting the variables for the nodes such

as the values that are applicable, or the state in which they are, and others. The discrete nodes

have been preferred here for discussion (Heckerman, 1998). Some of general discrete nodes

types are Boolean nodes, ordered nodes, and integral nodes. The Boolean nodes refer to the

would not reach feasible solution.

As per the inference is concerned, there are three of these within BN. They are given below:

Inferring unobserved variables

Due to the presence of all the observed variables in the Bayesian Network, it becomes easier

to infer the variables that are unobserved. Answering the queries with the help of probability

becomes easier (Murphy, 2002).

Parameter learning

Parameters are used to show the likelihood of one cause over another. The parameters are

generally unknown and require estimation.

Structure learning

The structures are defined in BNs with the help of experts and then inferences are derived.

Data are used to form the structure as in most cases it becomes challenging due to its

complexity.

The construction of Bayesian Networ requires understanding few steps. These steps are given

below:

Nodes and values

This is the first step where the individual tries to understand the variables that are into play.

There are some questions that are considered while selecting the variables for the nodes such

as the values that are applicable, or the state in which they are, and others. The discrete nodes

have been preferred here for discussion (Heckerman, 1998). Some of general discrete nodes

types are Boolean nodes, ordered nodes, and integral nodes. The Boolean nodes refer to the

nodes that propose something. For instance, if an individual has short breath and goes to the

doctor then there can be tuberculosis, bronchitis, and cancer. The node showing cancer will

be the proposition. On the other hand, if the pollution is the likely reason then the exposure

level has to be shown that can be represented by low, medium and high. This representation

shows the Ordered Values. The last one, integral values, shows the numerical value such as

the node showing the age of that patient.

This stage of model formation, modelling choices can be taken. For instance, instead of the

representation of the age of the patient on the nodes, the patient can be placed into certain age

group such as baby, adolescent, young and others. The selection of whatever values have

been done, the focus should be clearly representing the area.

Structure

The structure of the network needs to consider the relationships among the variables. The

nodes that are related directly in the network need to be directly connected. The direct

relation can be in the form of cause and effect. The arc should be there that shows which one

is causing what. The previous example can be taken to understand this aspect. If it is expected

that the pollution is the possible cause of the presence of cancer, then the tail of the arc

should be on the node representing pollution and the arrow point forward should be on the

cancer node. Understanding the terminologies in the construction of the nodes is also

important. There are generally four family associated terms used, namely, child, parents,

ancestors, and descendants. The node in front of a node is called as child and that particular

node will be parent to that child node. The earlier nodes will be called as ancestors and the

nodes ahead of the child will be called as descendants.

Conditional Probabilities

doctor then there can be tuberculosis, bronchitis, and cancer. The node showing cancer will

be the proposition. On the other hand, if the pollution is the likely reason then the exposure

level has to be shown that can be represented by low, medium and high. This representation

shows the Ordered Values. The last one, integral values, shows the numerical value such as

the node showing the age of that patient.

This stage of model formation, modelling choices can be taken. For instance, instead of the

representation of the age of the patient on the nodes, the patient can be placed into certain age

group such as baby, adolescent, young and others. The selection of whatever values have

been done, the focus should be clearly representing the area.

Structure

The structure of the network needs to consider the relationships among the variables. The

nodes that are related directly in the network need to be directly connected. The direct

relation can be in the form of cause and effect. The arc should be there that shows which one

is causing what. The previous example can be taken to understand this aspect. If it is expected

that the pollution is the possible cause of the presence of cancer, then the tail of the arc

should be on the node representing pollution and the arrow point forward should be on the

cancer node. Understanding the terminologies in the construction of the nodes is also

important. There are generally four family associated terms used, namely, child, parents,

ancestors, and descendants. The node in front of a node is called as child and that particular

node will be parent to that child node. The earlier nodes will be called as ancestors and the

nodes ahead of the child will be called as descendants.

Conditional Probabilities

The next step in the construction of BN requires quantification of the relationship among the

nodes. The conditional probabilities are used to fulfil this requirement. In this probabilistic

values are defined for each of the nodes then they will show the strengths that one node

impacts the other.

The Markov Property

The Markov Property is considered while forming the network. The Markov Property states

that if there does not exist any arc between two nodes, and the particular node is free of

dependencies, then any other form of dependencies should not be taken into consideration.

However, if the arc present in the model tries to show some dependencies, then it should not

be construed that there exists some interdependencies.

Bayesian Networks are needs to be converted into the Junction Trees for inference because

helps in universally applying the algorithm without any directional constraint. There are three

steps in total, they are:

- In first step, undirected graph is formed from the directed graph

- In the second step, variables are defined.

- In the third step, graphs that are not chordal are considered.

The connection of automatic BN construction to Machine Learning is that we involve in the

formulation of knowledge regarding particular situation in probabilistic way. To do this we

gather the data. After that, the posterior probability is computed for the parameters

(Heckerman et al, 1995). After that, this posterior distribution is utilized to identify scientific

conclusions, predicting, and forming decisions to reduce the posterior loss.

References

Jensen, F. V. (1996). An introduction to Bayesian networks (Vol. 210). London: UCL press.

nodes. The conditional probabilities are used to fulfil this requirement. In this probabilistic

values are defined for each of the nodes then they will show the strengths that one node

impacts the other.

The Markov Property

The Markov Property is considered while forming the network. The Markov Property states

that if there does not exist any arc between two nodes, and the particular node is free of

dependencies, then any other form of dependencies should not be taken into consideration.

However, if the arc present in the model tries to show some dependencies, then it should not

be construed that there exists some interdependencies.

Bayesian Networks are needs to be converted into the Junction Trees for inference because

helps in universally applying the algorithm without any directional constraint. There are three

steps in total, they are:

- In first step, undirected graph is formed from the directed graph

- In the second step, variables are defined.

- In the third step, graphs that are not chordal are considered.

The connection of automatic BN construction to Machine Learning is that we involve in the

formulation of knowledge regarding particular situation in probabilistic way. To do this we

gather the data. After that, the posterior probability is computed for the parameters

(Heckerman et al, 1995). After that, this posterior distribution is utilized to identify scientific

conclusions, predicting, and forming decisions to reduce the posterior loss.

References

Jensen, F. V. (1996). An introduction to Bayesian networks (Vol. 210). London: UCL press.

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Nielsen, T. D., & Jensen, F. V. (2009). Bayesian networks and decision graphs. Springer

Science & Business Media.

Heckerman, D., Geiger, D., & Chickering, D. M. (1995). Learning Bayesian networks: The

combination of knowledge and statistical data. Machine learning, 20(3), 197-243.

Heckerman, D. (1998). A tutorial on learning with Bayesian networks. In Learning in

graphical models (pp. 301-354). Springer Netherlands.

Murphy, K. P. (2002). Dynamic bayesian networks: representation, inference and learning

(Doctoral dissertation, University of California, Berkeley).

Science & Business Media.

Heckerman, D., Geiger, D., & Chickering, D. M. (1995). Learning Bayesian networks: The

combination of knowledge and statistical data. Machine learning, 20(3), 197-243.

Heckerman, D. (1998). A tutorial on learning with Bayesian networks. In Learning in

graphical models (pp. 301-354). Springer Netherlands.

Murphy, K. P. (2002). Dynamic bayesian networks: representation, inference and learning

(Doctoral dissertation, University of California, Berkeley).

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