The absence of familiarity with the correlation or mutual dependence between random variables complicates the process of creating probabilistic models in AI. Measuring the conditional probability of such an event might be a challenge, even if it is present. As a result, developers often rely on assumptions to handle such situations, like assuming that all random variables in the model are conditionally independent. This approach is commonly used in artificial intelligence and is the basis of Bayesian networks, which are probabilistic models that depend on random variables that are conditionally independent.
In this article, we will examine the workings of Bayesian networks in artificial intelligence by using an example. Furthermore, we will explore the various applications of this technique.
A Bayesian Networks Primer for Artificial Intelligence
A Bayesian network, also known as a causal network or belief network, is a probabilistic graphical model used to assess the probability of a given outcome. This type of network is acyclic, meaning there is no shortest route from one node to another. A Directed Acyclic Graph (DAG) accompanied by a probability table is utilised to calculate the likelihood of a given occurrence. Edges are used to connect the nodes of a Bayesian network, and the probability table shows the various probabilities of outcomes for a random variable.
An example of a Directed Acyclic Graph (DAG) can be seen in the top picture. The graph consists of five vertices, labelled A, B, C, D, and E. By analysing the chart, the following data can be obtained:
- In this case, node an is the parent of nodes b, c, and e, and these nodes are the children of node a.
- There are two nodes, b and c, that d descends from.
- E is a descendant of nodes D, C, and A.
It is essential to comprehend the links between the nodes in a Bayesian network. As a probabilistic graphical technique, probability is a fundamental factor in determining the interrelationships between the nodes.
In Bayesian networks, there are two kinds of probabilities that you must understand thoroughly:
The joint probability of two or more occurrences occurring simultaneously can be determined by calculating P(A∩B). As an illustration, if we have two occurrences, A and B, and we wish to calculate the likelihood of both occurring, we can do so by calculating P(A∩B).
Conditional probability is the measure of how likely it is that event B will happen if event A has already taken place.
A node table is a representation of the conditional probability distribution between two nodes, with the first row representing the potential values for the parent node (or “parent random variable”) and the second row representing the possible values for the child node (or “child random variable”). This table provides a means of visualising the relationship between the two nodes and understanding the probability of a certain outcome given a certain input.
For this table, each row presents a possibility of a parent and child combination. By summing up the chances of each of these possible outcomes, we can determine the likelihood of an event occurring.
Applying Bayesian networks to AI
To clarify, consider this illustration.
The residence is now fitted with a state-of-the-art burglar alarm system, which has been calibrated to detect even the slightest tremors as well as any potential break-ins. In the event that the burglar alarm is activated, your neighbours Chris and Martin will be alerted and will contact you. Chris should hear the alarm but may misinterpret it for the sound of the telephone ringing, and thus call you instead. Martin, on the other hand, is an avid music enthusiast who often listens to his music at a high volume, thus making him prone to oversleeping and not responding to his alarm.
Calculate the likelihood of a break-in happening in the home based on the information available about who will and will not notify the police.
We may think of the nodes in a Bayesian network as independent variables.
Five distinct nodes may be identified.
- Burglary (B) (B)
- Earthquake (E) (E)
- Alarm (A) (A)
- Call from Chris ( C )
- After receiving a call from Martin (M)
Uses for Bayesian networks in artificial intelligence
Uses for Bayesian networks include a wide range of activities, including:
- Anti-Spam measures: Spam philtres are software applications created to detect and remove uninvited electronic mail. Bayesian spam philtres are used to decide if an email is spam or not; these philtres learn to recognise undesirable content by screening it out.
- Biomonitoring: Indicators can be utilised to ascertain the relative concentration of a particular substance within an individual’s body. Comparable concentrations can be ascertained from either a sample of blood or urine.
- Data mining: Information retrieval is a continuous process of obtaining data from databases, and Bayesian networks are an advantageous technique used in this process. This process is cyclical, necessitating us to frequently re-examine and define our research question in order to avoid being overwhelmed by the sheer volume of information.
- Processing images: Picture processing, a subfield of signal processing, involves performing a series of mathematical operations on an image in order to convert it into a digital format. This process can potentially enhance the quality of the original image. The source picture can be of any type, including a still image or a frame from a video.
- Regulation of Gene Activity: The use of Bayesian networks is becoming increasingly popular as a means of analysing and predicting gene regulatory networks and how single-nucleotide polymorphisms (SNPs) may influence cellular phenotypes. By utilising a set of mathematical equations, known as gene regulatory networks, researchers can gain an understanding of the connections between genes, proteins and metabolites, and how mutations may affect cellular and organismal growth.
- Supersonic Secret code: Turbo codes are a type of error correction code that enable data to be transmitted at extremely high speeds over long distances between error-correcting nodes in a network. This technology has been adopted in a wide variety of applications, including satellite transmissions, deep space missions, military communication systems, and civilian wireless communication systems such as WiFi and 4G LTE cellular telephone networks.
- File Organisation: Computer Science and Information Science often confront the challenge of assigning various classes to documents. This can be done through manual labour or algorithmic processing; however, manual labour is often time consuming. Consequently, it is more efficient and effective to utilise documentation algorithms to complete the task.
Bayesian networks, which fall within the category of probabilistic graphical models, have been defined and demonstrated in the field of machine learning. The first step of the belief network involves representing each world state as either true or false. Subsequently, conditional probabilities are employed to illustrate all possible state transitions. Finally, probabilities are assigned to each condition based on all potential observations.
When presented with an ensemble of additional random variables, a belief network can be interpreted as a means of making inferences about the corresponding set of random variables. The joint probability distribution for conditional probabilities is established by the assumptions of conditional independence.
In artificial intelligence, why are Bayesian networks so crucial?Bayesian networks are incredibly beneficial when attempting to identify solutions to problems with uncertain results. Due to the numerous unknowns associated with such scenarios, Bayesian networks make it possible to accurately predict outcomes and uncover correlations between various variables and events. This is accomplished through the utilisation of joint and conditional probabilities.
Difference between Markov and Bayesian networksAlthough both Bayesian networks and Markov networks contain nodes and edges, the way they are used is significantly different. Specifically, a Bayesian network is directed and acyclic, whereas a Markov network can be either undirected or acyclic.
Bayesian networks are used to predict what?For the express purpose of creating probabilistic models in Artificial Intelligence (AI), Bayesian networks have been developed. Such models are often complex in nature, incorporating several interconnected variables, which can make it difficult to determine the probability of an occurrence. However, with the help of Bayesian networks, the process of determining the joint and conditional probability between two occurrences is much simpler.
What causes Bayesian networks to be undirected?For their underlying probability distribution to be normalised to 1, Bayesian networks must be acyclic, so long as that distribution is known.