In AI, constructing probabilistic models can prove challenging if the link between random variables is unclear. This can make measuring conditional probability difficult, despite it being present. To counteract such scenarios, developers often resort to assuming that all variables in the model are conditionally independent. This method, which is frequently deployed in artificial intelligence, is foundational to Bayesian networks – a probabilistic modelling approach that depends on variables which are conditionally independent.
This piece aims to delve into the mechanics of Bayesian networks in the realm of artificial intelligence by utilising an example. Additionally, we will examine the diverse uses of this approach.
A Guide to Bayesian Networks for Artificial Intelligence
A Bayesian network, also referred to as a belief network or causal network, is a type of probabilistic graphical model that analyses the likelihood of a particular outcome. These models are acyclic, which means there is no shortest path from one node to another. To evaluate the probability of an occurrence, a Directed Acyclic Graph (DAG) is utilised in conjunction with a probability table. A Bayesian network links nodes using edges, while the probability table displays the likelihood of outcomes for a random variable.
The top image displays an example of a Directed Acyclic Graph (DAG). This graph is composed of five nodes, denoted as A, B, C, D, and E. By examining the diagram, we can extract the following information:
- In this instance, node an is the parent of nodes b, c, and e, and these nodes are categorised as the offspring of node a.
- Node d originates from two nodes – b and c.
- Node E is a progeny of nodes D, C, and A.
Understanding the connections between the nodes in a Bayesian network is crucial. As a graphical model for probability, calculating the likelihood is fundamental in determining the links between nodes.
To gain a comprehensive understanding of Bayesian networks, it’s important to comprehend two types of probabilities:
To determine the joint probability of two or more events occurring simultaneously, use the formula P(A∩B). As an example, let’s say we have events A and B, and we want to calculate the likelihood of them happening together. We can do this by computing P(A∩B).
Conditional probability measures the probability of event B occurring after event A has already occurred.
The node table is a depiction of the conditional probability distribution between two nodes. The first row displays the potential values for the parent node (or “parent random variable”), while the second row displays the possible values for the child node (or “child random variable”). This table offers a way to visualise the connection between the two nodes and determine the probability of a particular outcome given a particular input.
Each row in this table represents a potential combination of a parent and child. By adding up the probabilities of each of these potential outcomes, we can calculate the likelihood of an event taking place.
Implementing Bayesian networks in AI
To better understand, take a look at this example.
A top-of-the-line burglar alarm system has been installed at the residence. This system has been configured to detect even the slightest movements and alert in case of a potential break-in. If the alarm goes off, your neighbours Chris and Martin will be notified and will contact you. Chris may mistake the sound of the alarm for that of a ringing telephone and call you instead. Martin, on the other hand, enjoys listening to loud music and may sleep through his alarm.
Based on the details accessible about who will and won’t alert the authorities, determine the probability of a burglary occurring at the residence.
Consider the nodes in a Bayesian network as independent variables.
There are five distinct nodes that can be identified.
- Burglary (B)
- Earthquake (E)
- Alarm (A)
- Call from Chris (C)
- Call from Martin (M)
Applications of Bayesian networks in artificial intelligence
Bayesian networks are utilized for various purposes, including:
Anti-Spam measures:Anti-spam filters are software applications designed to detect and eliminate unsolicited emails. Bayesian spam filters evaluate whether an email is spam or not; by filtering out undesired content, these filters are trained to identify it.
Biomonitoring:Biomarkers can determine the relative levels of a specific substance in a person’s body. A sample of blood or urine can be used to determine equivalent concentrations.
Data mining:Data mining is an ongoing process of retrieving information from databases, and Bayesian networks are a useful technique employed in this process. Since this process is cyclical, we must continuously revisit and redefine our research questions to avoid getting inundated by the volume of data.
Image processing:Image processing, which is a subfield of signal processing, entails performing a sequence of mathematical operations on an image to convert it to a digital format. The quality of the original image can be improved by this process. The original image can be of any kind, such as a still image or a frame from a video.
Regulation of Gene Activity:Bayesian networks are increasingly being utilized to analyse and predict gene regulatory networks and how single-nucleotide polymorphisms (SNPs) can impact cellular phenotypes. By utilizing a set of mathematical equations referred to as gene regulatory networks, researchers can comprehend the relationships among genes, proteins, and metabolites, as well as how mutations may affect cellular and organismal development.
Supersonic Code:Turbo codes are a form of error correction code that enable data to be transmitted at extremely high speeds over lengthy distances between error-correcting nodes in a network. This technology is utilized in a variety of applications, including satellite transmissions, deep space missions, military communication systems, and civilian wireless communication systems like WiFi and 4G LTE cellular phone networks.
File Organization:Computer Science and Information Science are frequently faced with the task of categorizing various documents. Although this can be done manually, it is often time-consuming, and algorithmic processing is a more efficient and effective method.
Bayesian networks, which belong to the category of probabilistic graphical models, have been extensively studied in the field of machine learning. The first step in constructing a belief network is to represent each world state as either true or false. Subsequently, conditional probabilities are employed to depict all possible state transitions. Finally, probabilities are assigned to each condition based on all potential observations.
When confronted with a collection of additional random variables, a belief network can be used to make inferences about that set of random variables. The assumptions of conditional independence establish the joint probability distribution for conditional probabilities.
Why are Bayesian networks so crucial in artificial intelligence?When attempting to identify solutions to problems with uncertain outcomes, Bayesian networks are extremely useful. Because such situations contain numerous unknowns, Bayesian networks allow for precise prediction of outcomes and identification of correlations between different variables and events. Joint and conditional probabilities are used to achieve this.
Markov networks vs Bayesian networksDespite similarities in terms of containing nodes and edges, there are significant differences between Markov networks and Bayesian networks. Specifically, Bayesian networks are directed and acyclic, while Markov networks can be either undirected or acyclic.
What are Bayesian Networks used for prediction?Bayesian networks have been developed for the specific purpose of creating probabilistic models in Artificial Intelligence (AI). These models are frequently complex, incorporating numerous interrelated variables, making it challenging to determine the probability of an event occurring. Bayesian networks, on the other hand, make it much simpler to determine the joint and conditional probability between two events.
Why can Bayesian networks be undirected?Bayesian networks must be acyclic to ensure that their underlying probability distribution is normalized to 1, provided that the distribution is known.