4. Graphical Models & Probabilistic Inference
Graphical models serve as powerful tools for modeling complex systems with multiple variables by representing joint probability distributions through graphs. They integrate graph theory and probability theory to enhance probabilistic reasoning and inference in high-dimensional spaces. Various types of graphical models, including Bayesian networks, Markov random fields, and factor graphs, are examined alongside inference algorithms and learning methods, demonstrating their practical applications across diverse fields.
Sections
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What we have learnt
- Graphical models allow for the representation and analysis of joint probability distributions over multiple variables using graphs.
- Key types of graphical models include Bayesian networks, Markov random fields, and factor graphs, each serving different purposes.
- Inference in graphical models can be performed through exact methods, such as variable elimination and belief propagation, or through approximate methods, including sampling and variational inference.
Key Concepts
- -- Graphical Models
- A framework for representing joint probability distributions over variables using a graph structure, where nodes are random variables and edges depict dependencies.
- -- Bayesian Networks
- Directed graphical models that use directed acyclic graphs to represent conditional dependencies among variables.
- -- Markov Random Fields
- Undirected graphical models that express relationships through cliques, showcasing local dependencies among variables.
- -- Conditional Independence
- A fundamental concept stating that two variables are independent given a third, allowing for simpler factorization of distributions.
- -- Inference
- The process of computing probabilities or explaining observed data in the context of graphical models.
Additional Learning Materials
Supplementary resources to enhance your learning experience.