Creating a probabilistic model can be challenging but proves helpful in machine learning. To create such a graphical model, you need to find the probabilistic relationships between variables. Suppose you are creating a graphical representation of the variables. You need to represent the variables as nodes and conditional independence as the absence of edges. Graphical models such as Bayesian statistics models are growing popular in numerous fields for different tasks and activities. Some applications of graphical models are as follows:

• Weather forecasting
• Natural language processing
• Diagnosis and troubleshoot
• Medical monitoring
• Machine vision
• Digital communication
• Manufacturing
• Medical monitoring
• Genetic counseling
• Information retrieval

Probabilistic Model Challenges

When designing probabilistic models, you encounter numerous challenges in designing and using the graphical model. The most common problem that you might encounter is limited data. You need a domain and dedicate it for the conditional dependence among random variables. It would be unreasonable to calculate the complete conditional probability of an event.

You can address this challenge through various assumptions. For instance, you can simplify the assumption by assuming that all the random variables are conditionally independent. This approach will help you to practice with the algorithm such as Naive Bayes classification algorithm.

There are various solutions to create a probabilistic model. Bayesian networks are such models that work as an intermediate between a fully conditionally independent model and a fully conditional model.

What is Bayesian Network?

Bayesian networks enable you to deal with probabilistic events. Furthermore, this computer technology also helps in solving complex and uncertain problems. You might know Bayesian networks by Bayes network, decision network, belief network, or Bayesian model. Here is a proper definition of Bayesian networks for better understanding:

Bayesian networks represent random sets of variables and conditional dependencies of these variables on a graph. Bayesian network is a category of the probabilistic graphical model.

You can design Bayesian networks by a probability distribution that is why this technique is probabilistic distribution. Bayes network is the perfect solution for anomaly detection and predicting the events as it uses probability theory.

Bayesian networks enable you to characterize different variables and define the relationship between various events. Most real-world problems and applications are hard to solve. However, the nature of those applications is probabilistic. That is why we need a solution such as a Bayesian network. You can also use the Bayes network for the following tasks:

• Making decisions for uncertain factors
• Predicting time series
• Reasoning
• Diagnostics
• Prediction
• Automated insight
• Anomaly detection

While designing a graph with Bayesian networks’ help, you need to measure the nodes and links between those nodes. These are the two components that complete a Bayesian network.

Joint Probability Distribution

The joint probability distribution is the probability indicating the intersection of two events. You can also find the probability distribution of two random variables with this method. The main purpose of the joint probability distribution is to identify the relationship among two variables. In a Bayes model, when you have variables x1, x2, x3,…….,xn, the probabilities of these variables and their combination will be Joint probability distribution.

P[x1, x2, x3,…..,xn],

You can write the joint probability distribution as:

= P[x1| x2, x3,….., xn]P[x2, x3,….., xn]

= P[x1| x2, x3,….., xn]P[x2|x3,….., xn]….P[xn-1|xn]P[xn].

From the above explanation, we can represent the equation of joint probability distribution as below:

P(X_i|X_i-1,………, X₁) = P(X_i |Parents(X_i ))

Nodes

Every node available in Bayesian networks will represent a variable. These variables may be gender, age, or height. You can also subdivide these variables. For instance, you can divide the gender into male and female.

Furthermore, the variables can be continuous as people age. You can add multiple variables to every node. You can also refer to nodes as multi-variable nodes as the nodes include various variables.

A Bayes network is a structure of nodes and links. This network is a structural specification. There are both continuous and discrete variables in the Bayes server.

• Discrete Variable

There is a set of exclusive sub-variables in a discrete variable such as males and females are sub-variables of gender, which is itself a variable.

• Continuous Variable

The server also includes continuous variables as CLG or Conditional Linear Gaussian distribution. This indicates that the continuous distribution of variables or multivariate dependent on each other. Furthermore, these variants can also rely on single and multiple discrete variables.

Links

You can add links between nodes to represent the direct influence of one node on another. Two nodes without any link may have a connection with each other. Both these nodes are dependent on each other through other nodes and connections. Nodes may seem independent or dependent according to the evidence set by other nodes.

• Structural learning

Bayes Server enables you to determine links with the help of data automatically. This server contains a structural learning algorithm to support Bayesian networks.

Bayesian Statistics

Bayesian statistics help you express the degree of belief of an event through a probabilistic approach. Bayesian statistics is a statistical theory that includes a Bayesian interpretation of probability. The knowledge about an event will develop the degree of belief. Bayesian statistics is the only theory that considers probability as a degree of belief. However, other interpretations of probability differ with Bayesian statistics in that matter. For instance, frequentist interpretation considers probability as relative frequency limitation of an event after multiple trials.

You can use Bayesian statistical methods to compute and manage the probabilities based on new data. Bayes’ theorem helps in the development of computation and updating methods. Furthermore, Bayes theorem explains the event’s conditional probability with the help of data, previous information, and belief of these events and variables. For instance, you can estimate the statistical model or probability distribution parameters using the Bayes theorem in Bayesian inference. Bayes theorem enables you to assign the probability distribution and measure the belief parameters using Bayesian statistics.

Conclusion

Bayesian Networks is a probabilistic graphical model that enables you to solve a complex problem. This network helps you state conditional independence of the variables you already know and share information and links about unknown variables.