Introduction: Bayesian Networks (BNs), also known as Bayesian Belief Networks or Bayesian Directed Acyclic Graphs (DAGs), are probabilistic graphical models that represent a set of random variables and their conditional dependencies via a directed acyclic graph. These networks are widely used in various fields, including Artificial Intelligence, as powerful tools for reasoning under uncertainty.
Objective: The primary objective of this practical is to equip students with the knowledge and skills to construct a Bayesian Network from given data. This involves understanding the underlying probabilistic relationships between variables and utilizing this information to build a graphical model that accurately represents these dependencies.
Theory:
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Bayesian Networks Overview:
- A Bayesian Network consists of nodes and directed edges. Nodes represent random variables, and directed edges represent probabilistic dependencies.
- The network structure is acyclic, preventing the occurrence of loops, ensuring a clear causal direction.
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Conditional Independence:
- Fundamental to Bayesian Networks is the concept of conditional independence. A node is conditionally independent of its non-descendants given its parents.
- This property significantly reduces the number of parameters needed to specify the joint probability distribution of the variables.
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Nodes and Variables:
- Nodes in a Bayesian Network correspond to variables. These can be discrete or continuous, depending on the nature of the data.
- Variables are classified into three types: observable (input), hidden (latent), and evidence (observed).
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Probabilistic Dependencies:
- The edges between nodes represent probabilistic dependencies. Each node is associated with a conditional probability distribution given its parents.
- The joint probability distribution of all variables is the product of these conditional distributions.
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Parameterization:
- Parameters in a Bayesian Network are probabilities. Conditional Probability Tables (CPTs) specify the probability distribution of a node given its parents.
- Learning these parameters from data is a crucial step in building a Bayesian Network.
Steps in Constructing a Bayesian Network:
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Identify Variables:
- Determine the variables in the domain and their relationships.
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Define Structure:
- Establish the structure of the network by identifying the dependencies between variables. This is often based on domain knowledge or statistical analysis.
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Parameterize the Network:
- Assign probabilities to the nodes based on the observed data. This involves constructing Conditional Probability Tables (CPTs).
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Verify and Refine:
- Validate the network against the data and refine as necessary. Bayesian Networks are iterative models that can be improved with additional information.
Conclusion: Constructing a Bayesian Network from data is a valuable skill in the field of Artificial Intelligence. It allows for efficient representation of probabilistic relationships and facilitates reasoning under uncertainty. This practical aims to provide students with hands-on experience in building these networks, enhancing their understanding of probabilistic graphical models.
Dataset is available on https://www.kaggle.com/datasets/cherngs/heart-disease-cleveland-uci