## Graphical Models

author: Christian Borgelt, European Center for Soft Computing
published: Oct. 5, 2007,   recorded: September 2007,   views: 1166
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# Slides

0:00 Slides A Tutorial on Graphical Models and How to Learn Them from Data Overview Graphical Models: Core Ideas and Notions A Simple Example: The Relational Case A Simple Example The Reasoning Space The Relation in the Reasoning Space Reasoning Prior Knowledge and Its Projections Cylindrical Extensions and Their Intersection Reasoning with Projections Using other Projections pt 1 Using other Projections pt 2 Is Decomposition Always Possible? Relational Graphical Models: Formalization Possibility-Based Formalization pt 1 A Tutorial on Graphical Models and How to Learn Them from Data (a) Possibility-Based Formalization pt 1 (a) Possibility-Based Formalization pt 2 Possibility-Based Formalization pt 3 Relational Decomposition: Simple Example Possibility-Based Formalization pt 3 (a) Possibility-Based Formalization pt 1 (b) Possibility-Based Formalization pt 3 (b) Conditional Possibility and Independence Conditional Independence: Simple Example Relational Evidence Propagation Relational Evidence Propagation, Step 1 Relational Evidence Propagation (a) Relational Evidence Propagation, Step 1 (a) Relational Evidence Propagation (b) Relational Evidence Propagation, Step 1 (continued) Relational Evidence Propagation, Step 2 A Simple Example: The Probabilistic Case A Probability Distribution Reasoning: Computing Conditional Probabilities A Probability Distribution (a) Reasoning: Computing Conditional Probabilities (a) Probabilistic Decomposition: Simple Example Reasoning with Projections Probabilistic Graphical Models: Formalization Probabilistic Decomposition Probabilistic Decomposition: Simple Example (a) Conditional Independence Probabilistic Decomposition (continued) Conditional Independence (a) Probabilistic Decomposition (continued) (a) Conditional Independence: An Example pt 1 Conditional Independence: An Example pt 2 Conditional Independence: An Example pt 3 Conditional Independence: An Example pt 1 (a) Conditional Independence: An Example pt 2 (a) Reasoning with Projections Probabilistic Evidence Propagation, Step 1 Probabilistic Evidence Propagation, Step 1 (continued) Probabilistic Evidence Propagation, Step 2 Graphical Models: The General Theory (Semi-)Graphoid Axioms Illustration of the (Semi-)Graphoid Axioms Separation in Graphs Separation in Directed Acyclic Graphs Conditional (In)Dependence Graphs Limitations of Graph Representations Markov Properties of Undirected Graphs Markov Properties of Directed Acyclic Graphs Equivalence of Markov Properties Undirected Graphs and Decompositions

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Part 2 28:34

# Description

In the last decade probabilistic graphical models -- in particular Bayes networks and Markov networks -- became very popular as tools for structuring uncertain knowledge about a domain of interest and for building knowledge-based systems that allow sound and efficient inferences about this domain. The lecture gives a brief introduction into the core ideas underlying graphical models, starting from their relational counterparts and highlighting the relation between independence and decomposition. Furthermore, the basics of model construction and evidence propagation are discussed, with an emphasis on join/junction tree propagation. A substantial part of the lecture is then devoted to learning graphical models from data, in which quantitative learning (parameter estimation) as well as the more complex qualitative or structural learning (model selection) are studied.

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