Unit 1.5 | Markov Networks | AAI | Undirected Graphs, Factors, Partition Function, Cliques

Описание: This video explains Unit 1.5 – Markov Networks (Undirected Graphical Models) from the AAI syllabus. It introduces an alternative probabilistic graphical model used to represent relationships where interactions are symmetric and do not have a clear direction.

The lecture begins by discussing the limitations of Directed Graphical Models (Bayesian Networks) in representing certain types of relationships. In many real-world scenarios, variables influence each other equally, making undirected graphs more suitable for modeling such dependencies.

Next, the video explains how Markov Networks use factors instead of Conditional Probability Distributions (CPDs). These factor functions (ϕ) represent the compatibility or affinity between variables connected in the graph.

Since factor values are not direct probabilities, the model computes the joint probability distribution by multiplying all factors and dividing by a normalization constant called the Partition Function (Z).

The lecture also introduces the concept of Maximal Cliques, which are fully connected subsets of nodes in the graph. Instead of defining factors only between pairs of variables, factors are assigned to maximal cliques, allowing the network to efficiently represent complex relationships.

Finally, the video explains how these clique-based factors define a Gibbs Distribution, which forms the mathematical foundation of Markov Networks.

The explanation is provided in simple language with clear examples, making it useful for AI, Machine Learning, and Computer Engineering students.

Topics Covered:

Introduction to Markov Networks

Limitations of Bayesian Networks

Undirected Graphical Models

Factor Functions (ϕ)

Joint Probability Computation

Partition Function (Z)

Maximal Cliques in Graphical Models

Gibbs Distribution in Markov Networks

This lecture helps build a strong understanding of probabilistic graphical models used in Artificial Intelligence and Machine Learning.