Bayesian Networks

Bayesian Networks

What are Bayesian Networks?

Bayesian networks are a kind of probabilistic graphical standard that uses the Bayesian hypothesis for probability calculations. Bayesian networks seek to enable conditional dependence, and therefore causation, by defining conditional dependence by edges in a digraph. By drawing relationships between metrics, one can efficiently accomplish inference on the random variables in the graph through the consideration of factors.

A Bayesian Network is a simple method of applying the Bayes Theorem to real-world problems. Bayes’ Theorem states that the dependent probability of an occurrence, founded on the event of another occurrence, is equivalent to the probability of the second event given the first occurrence multiplied by the possibility of the first event.

Even though the networks are not the exact derivations of Bayesian, both are probability distributions for random variables (nodes) and relationships between those random variables (edges). Each of these is represented subjectively and the model can then capture the intent of complex space.

What is Bayesian Probability in Bayesian Networks?

Bayesian probability is the study of impressionistic probabilities in an effect, in contrast to the frequentist type of probability computations which are based purely on past events and affect. A Bayesian Network captures these joint probabilities of the circumstances represented by the model. It also describes the mutual probability distribution for a group of variables, central to these networks is the concept of conditional independence. Independence here is random variables that are unaffected by the other values. Dependent variables also exist whose probability is conditional on other random variables.

Conditional independence represents the connections among numerous random variables, where a certain value may be conditionally disconnected from other random variables. This does not directly convey that the value condition is independent; instead, it denotes that the variable is separate from distinct known random variables.

What are the Advantages of Bayesian Network as a Graphical Model?

graphical model (GM) is a method of representing a collective distribution by making Conditional Independence-CI assumptions. Most times, the nodes in the graph denote random variables, and the (absence of) edges depict CI assumptions. Such a probabilistic graphical model (Bayesian Network) enables a method to define a difficult problem by expressing all of the conditional independence assumptions for the known variables, but also provides a hollow representation denoting the presence of unknown (latent) variables.

As determined directly from the real world, both the presence and the absence of edges in the graphical model play a crucial role in the interpretation of the model.

For example:

• Visualization. The model supports the ability to directly visualize the structure of the model and encourages the design of new models.
• Relationships. The model enables insight generation that helps navigate the presence and absence of the relationships between arbitrary values.
• Computations. the model’s make-up supports a method to structure complex probability calculations.

How are Bayesian Networks Developed?

Developing a Bayesian Network needs complete analysis and understanding in these three key areas:

• Random Variables. What are the random variables from the defined problem?
• Conditional Relationships. What are the conditional relationships among these random variables?
• Probability Distributions. What are the probability distributions per variable?

Although it is rarely possible to identify some or all of these aspects to design the model, an expert in the problem domain can define the architecture or topology of the graphical model by themselves, but the estimations of the probability distributions must be performed by the domain directly.

In regards to the data sets, the probability distributions and the graph structure can be determined, in most cases, intelligent learning algorithms are used for this purpose;

Once a Bayesian Network is composed and ready for a domain, it can be utilised for reasoning, e.g. making decisions.

The reasoning process is achieved through inference with the model for a particular circumstance. For instance, the result for an event is known and input into the random variables. The model can then be operated to perform estimations to determine the cause of the events or compute further possible outcomes. The reasoning is applied by introducing known states of a random event, this in return helps position the random variables and subsequently compute probabilities of interest for a given state.

A unique property of Bayesian Networks is that the circumstance of all the parents of a node will ensure the occurrence of the child. In mathematical terms: This makes the sub-networks of a Bayesian Network consistent, which means that the child networks derived are also Bayesian Networks.

Where are Bayesian Networks used?

Here are a few Practical examples of using Bayesian Networks in practice:

Spam Filter: A spam filter is a program used to detect unsolicited and unwanted emails, calls, or any type of new information. Bayesian spam filter estimates whether the transmission is spam or not. A Bayesian spam filter system is more robust since it performs these filtering actions by learning from historic data as well as new trends in spam filter texts and ham messages.

Information Retrieval: It is the process of acquiring information resources from databases. Since it is a continuous process the consideration, reconsideration and refining of the problem and data are very important. Bayesian netoworks helps reduce “information overload“ by using automated information retrieval systems.

Semantic Search: By precisely analysing searcher intent and understanding the contextual meaning of keywords, the Bayesian network improves search accuracy. It improves the accuracy of the searchable dataspace to produce more relevant results.

Image Processing: Bayesian networks help the mathematical operations carried out in the processing of images like signal processing, this signal processing input can an image while the output can be exported as a set of characteristics or parameters related to the image or an image. With such image processing techniques, the image is treated as a two-dimensional signal, after which, standard signal processing using bayesian networks is applied to it for processing or conversion.

Biomonitoring: Biomonitoring is used to quantify the concentration of chemicals, this can be the concentration in blood and tissue of humans, etc. Hence Bayesian Networks play a huge role in analytical chemistry used to process complex ratios of chemicals in a given sample.

Document Classification: Algorithmic classification of documents is performed through the robust implementation of Bayesian Networks in the classification system.

Turbo Code: These codes are a type of high-performance forward error correction code that uses the Bayesian Network. 3G and 4G telephony standards use these codes for turbo coding and decoding process.

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