Everyday Data Science professionals solve numerous problems with the help of newly developed and sophisticated AI technologies, Machine Learning and Advanced analytics. The main objective while solving these problems is to offer very reliable and error-free results. But it is important to present a list of actionable drivers of the model output used by end-users in making business decisions when applying these techniques. This criterion extends to industry-wide solutions. The Bayesian Belief Network, the subject of this blog, is one such machine-learning process that focuses on providing this actionable insight.
Let’s explore it in detail.
Table of Contents
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:
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.
There are many Bayesian belief network advantages and disadvantages. They are listed below:
There are a few advantages of Bayesian belief networks as it visualizes different probabilities of the variables. Some of them are:
To build a Bayesian network, you have to ask three questions yourself:
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.
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:
We know that C and A are independent of each other.
We can also define the conditional independencies as:
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(A|C, B) = P(A|B)
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(A|B), P(C|B)) or P(B).
We can also write the joint probability of A and C were given B, for example:
P(A, C | B) = P(A|B) * P(C|B)
The model bridges the joint probability of P(A, B, C), estimated as:
P(A, B, C) = P(A|B) * P(C|B) * P(B)
We can draw the graph as follows:
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.
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:
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.
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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