Unit I

Probabilistic Graphical Model (PGM) Definition

A Probabilistic Graphical Model (PGM) is a powerful framework for representing and reasoning about complex systems characterized by uncertainty. It combines graph theory and probability theory to:

• Model the relationships: Between variables using a graph structure, where nodes represent variables and edges represent their dependencies.
• Quantify uncertainty: By assigning probability distributions to each variable and its combinations, capturing the level of confidence in their values.
• Reason and predict: Using efficient algorithms to infer hidden states, make predictions about future events, and perform learning tasks.

Key characteristics of PGMs:

• Declarative: Focuses on "what" the relationships are rather than "how" they are implemented.
• Probabilistic: Quantifies uncertainty about variables and their relationships.
• Graphical: Uses graphs to visualize dependencies and interactions between variables.

Types of PGMs:

• Bayesian Networks: Use directed acyclic graphs (DAGs) with causal relationships between variables.
• Markov Networks: Use undirected graphs with dependencies between variables.

Applications of PGMs:

• Machine learning: Classification, regression, anomaly detection, recommender systems.
• Computer vision: Image segmentation, object recognition, scene understanding.
• Bioinformatics: Gene expression analysis, protein-protein interaction networks, disease prediction.
• Natural language processing: Part-of-speech tagging, sentiment analysis, machine translation.

Benefits of using PGMs:

• Intuitive representation: Simplifies understanding complex relationships through visualization.