 What is the Bayesian Belief Network?
 What are the Bayesian Networks used for?
 Bayesian belief network advantages and disadvantages
 How to develop and use a Bayesian Belief Network
 Mathematical Definition of Belief Networks
 How can we use Bayesian Networks in SNA?
1. What is the Bayesian Belief Network?
Bayesian belief network is a useful way to represent probabilistic models and visualize them. Before we get into Bayesian networks, let us understand probabilistic models.
Probabilistic models determine the relationship between variables, and then you can calculate the various probabilities of those two values. Bayesian Network is also called a Probabilistic Graphical Model (PGM).
For example, conditional models need a massive amount of information and data to calculate all possible outcomes, and putting all those possibilities to experiment is difficult. Simplifying these probabilities of all the random variables proves to be effective.
Bayesian networks are such visual probabilistic models that depict the conditional dependence of different variables in a graph. All the gaps and inconsistencies describe the conditional independencies in the graph. It is a powerful tool to visualize probabilities, understand and analyze the relationship between random variables and the possibilities for different situations.
Here, we list out how the process works:
 A Bayesian network operates on the Bayes theorem. The theorem is mostly applied to complex problems. This theorem is the study of probabilities or belief in an outcome, compared to other approaches where probabilities are calculated based on previous data. Bayesian Network works on dependence and independence.
 Independence means a random number or variable that is not affected by other variables. A dependence or dependent variable is also a random variable, but its probability is uncertain, and it depends on other variables.
 The term conditional independence is used in this network to determine the relationship between different random variables. The variable can be conditional independent.
2. What are the Bayesian Networks used for?
Bayesian Networks can be useful in many streams. Application of Bayesian belief network happens in the stream of an optimized search engine, diagnosis of different diseases, filtering spam emails, gene regulatory networks, and a lot more.
The main aim of this network is to understand the concept of causality relations. To begin with, let’s think of this as a diagnosis of a disease. The symptoms are in front of your eyes, and you can determine the condition by seeing the symptoms. The Bayesian Belief network works similarly to detecting disease by examining symptoms. For example, when a new patient comes, you determine possible diseases they might have after checking their symptoms. The network is also providing the probabilities for every single disease.
Such causality relations can be developed for other logical problems and inferences as well to obtain impressive results.
The Bayesian belief network meaning determines the relationships between numbers and variables and what possible outcomes can come out of it.
The functioning of a Bayesian belief network
A Bayesian network is made of nodes and arcs. Let’s understand what is Bayesian belief network explained in simple words.
 Each node represents the random variables, and a variable can be discrete or continuous.
 Directed arrows or arcs correspond to the causal relationship between the variables. These directed links connect the pair of nodes in the graphical model.
 In these links, one node directly affects the other node, and if there is no direct link, the variables are independent of each other.
(source: https://www.javatpoint.com/bayesianbeliefnetworkinartificialintelligence)
3. Bayesian belief network advantages and disadvantages
There are many Bayesian belief network advantages and disadvantages. They are listed below:
Advantages
There are a few advantages of Bayesian belief network as it visualizes different probabilities of the variables. Some of them are:
 Graphical and visual networks provide a model to visualize the structure of the probabilities and develop designs for new models as well.
 Relationships determine the type of relationship and the presence or absence of it between variables.
 Computations calculate complex probability problems efficiently.
 Bayesian networks can investigate and tell you whether a particular feature is taken into a note for the decisionmaking process and can force to include that feature if necessary. This network will ensure that all known features are investigated for deciding on a problem.
 Bayesian Networks are more extensible than other networks and learning methods. Adding a new piece in the network requires only a few probabilities and a few edges in the graph. So, it is an excellent network for adding a new piece of data to an existing probabilistic model.
 The graph of a Bayesian Network is useful. It is readable to both computers and humans; both can interpret the information, unlike some networks like neural networks, which humans can’t read.
Disadvantages
 The most significant disadvantage is that there is no universally acknowledged method for constructing networks from data. There have been many developments in this regard, but there hasn’t been a conqueror in a long time.
 The design of Bayesian Networks is hard to make compared to other networks. It needs a lot of effort. Hence, only the person creating the network can exploit causal influences. Neural networks are an advantage compared to this, as they learn different patterns and aren’t limited to only the creator.
 The Bayesian network fails to define cyclic relationships—for example, deflection of airplane wings and fluid pressure field around it. The deflection depends on the pressure, and the pressure is dependent on the deflection. It is a tightly coupled problem which this network fails to define and make decisions.
 The network is expensive to build.
 It performs poorly on high dimensional data.
 It is tough to interpret and require copula functions to separate effects and causes.
4. How to develop and use a Bayesian Belief Network
To build a Bayesian network, you have to ask three questions yourself:
 Variables: what are the random variables in my project?
 Conditional dependencies: what are the relationships between the variables, and are they independent or dependent?
 Probability Dispersals: how is the probability of each variable distributed in my project?
An expert can answer all these questions to you and even suggest a design for the Bayesian Belief Network model. Usually, experts define the architecture of such models, but you have to determine the probability distributions from the given data. The probability distributions and the graph structure can be calculated from the data, but it is a complicated process.
You can use algorithms to calculate the graph; for example, assume a Gaussian distribution for continuous variables that are random to calculate the distribution parameters.
After the Bayesian Belief Network is ready for any domain, you can use it for logical reasoning like getting answers to situational problems and making decisions.
The reasoning is accomplished by interpretation done by the model for a given problem or situation. For example, if the outcome for some events is known, then the model automatically calculates all the probabilities of causes for the events and other possible outcomes.
5. Mathematical Definition of Belief Networks
The mathematical definition is given as:
From the above formula, the conditional relationship is determined. We have to calculate the joint distribution. It is easier to understand the Bayesian belief network with examples.
Python Example of Belief Network
Bayesian Networks are popularly used to interpret Python programming language.
You can refer to PyMC, a massive library that provides a wide range of tools to build Bayesian networks, consisting of graphical models. The current version of this library is PyMC3 for Python version 3. It was created on Theano mathematical computation library that provides automatic differentiation.
Let us take three random variables: A, B, and C. A is a dependent variable on B, and C is a dependent variable on B.
We can define the conditional dependencies as:
 A is conditionally dependent upon B, like P(AB)
 C is conditionally dependent upon B, like P(CB)
We know that C and A are independent of each other.
We can also define the conditional independencies as:
 A is conditionally independent of C: P(AB, C)
 C is conditionally independent of A: P(CB, A)
You will notice that the dependencies are mentioned in the presence of independent variables. A is independent of C conditional, but it is dependent on B conditionally in the presence of C.
We can also define the independence of A given C as the dependent variable conditionally in the presence of B, as A is unaffected by C and can be calculated from A given B alone.
P(AC, B) = P(AB)
You will see B is not affected by A and C and has no parents, so you can determine the independence of B from A and C as P(B, P(AB), P(CB)) or P(B).
We can also write the joint probability of A and C were given B, for example:
P(A, C  B) = P(AB) * P(CB)
The model bridges the joint probability of P(A, B, C), estimated as:
P(A, B, C) = P(AB) * P(CB) * P(B)
We can draw the graph as follows:
(source: https://machinelearningmastery.com/introductiontobayesianbeliefnetworks/)
The random variables are given a mode, and the conditional relationships are defined as direct connections between the nodes. A graph cannot be navigated in a cycle; for example, loops are impossible when steering from one node to another via edges.
The graph is useful even now when you don’t know about probability distributions for the variables.
6. How can we use Bayesian Networks in SNA?
In SNA, you try to decode and understand the structure of a social network. You can also comprehend the nodes’ significance, but we don’t know the outcome of the network’s decision. Then, the Bayesian belief network comes into the picture; for example, if you think the significance of a node is happened by Degree Centrality and Link Centrality by the following:
(source: https://towardsdatascience.com/introductiontobayesianbeliefnetworksc012e3f59f1b)
It is a basic graph to understand how Bayesian Network is applied in Social Network Analysis.
Another example is for friend groups; for example, the groups in a social network are members of the group, and some of them might be friends as well. So, there will be two nodes – friends in the group and members in the group connected in a common group.
This concept is very new in Bayesian networks, and many scientists and experts are researching it.
Conclusion
Bayesian networks are used in Artificial Intelligence broadly. It is used in many tasks like filtering your email account from spam mails. It is also used in creating turbo codes and in 3G and 4G networks. It is used in image processing –they convert images into different digital formats. It also has a massive contribution to medical science and biotechnology like Biomonitoring, through which it can determine the number of tissues present in our body through indicators. Bayesian Networks also make the basis of Gene Regulatory Network. It has proven to be a useful and impactful network among many other networks and is developing each day with engineers and experts working on it to make it more efficient.
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