The chapter introduces graphical models, a powerful methodology for handling complex probabilistic models in various fields such as bioinformatics, information retrieval, and speech processing. Graphical models represent probability distributions using directed or undirected graphs, where nodes correspond to random variables and edges represent dependencies. The chapter covers the basic concepts of graphical models, including the representation of joint probability distributions and the algorithms for probabilistic inference. Key topics include: 1. **Representation**: Directed graphical models use directed acyclic graphs (DAGs), while undirected graphical models use undirected graphs. Both types of models capture conditional independence structures. 2. **Algorithms for Probabilistic Inference**: The chapter discusses exact algorithms like the elimination algorithm, sum-product algorithm, and junction tree algorithm, which exploit the graphical structure to compute marginal and conditional probabilities efficiently. 3. **Sampling Algorithms**: Methods like importance sampling and Markov Chain Monte Carlo (MCMC) are introduced, which are useful for approximate inference in complex models. 4. **Variational Algorithms**: These algorithms approximate the true posterior distribution by solving an optimization problem, often involving the minimization of a divergence measure like the Kullback-Leibler divergence. The chapter also provides examples of graphical models in action, particularly in bioinformatics, including phylogenetic trees and pedigrees, demonstrating how these models can be used to model and analyze biological data.The chapter introduces graphical models, a powerful methodology for handling complex probabilistic models in various fields such as bioinformatics, information retrieval, and speech processing. Graphical models represent probability distributions using directed or undirected graphs, where nodes correspond to random variables and edges represent dependencies. The chapter covers the basic concepts of graphical models, including the representation of joint probability distributions and the algorithms for probabilistic inference. Key topics include: 1. **Representation**: Directed graphical models use directed acyclic graphs (DAGs), while undirected graphical models use undirected graphs. Both types of models capture conditional independence structures. 2. **Algorithms for Probabilistic Inference**: The chapter discusses exact algorithms like the elimination algorithm, sum-product algorithm, and junction tree algorithm, which exploit the graphical structure to compute marginal and conditional probabilities efficiently. 3. **Sampling Algorithms**: Methods like importance sampling and Markov Chain Monte Carlo (MCMC) are introduced, which are useful for approximate inference in complex models. 4. **Variational Algorithms**: These algorithms approximate the true posterior distribution by solving an optimization problem, often involving the minimization of a divergence measure like the Kullback-Leibler divergence. The chapter also provides examples of graphical models in action, particularly in bioinformatics, including phylogenetic trees and pedigrees, demonstrating how these models can be used to model and analyze biological data.