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Graphical Models
Published on Oct 05, 20079749 Views
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 an
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Chapter list
A Tutorial on Graphical Models and How to Learn Them from Data00:00
Overview01:09
Graphical Models: Core Ideas and Notions03:16
A Simple Example: The Relational Case08:35
A Simple Example09:31
The Reasoning Space11:26
The Relation in the Reasoning Space12:04
Reasoning12:33
Prior Knowledge and Its Projections13:45
Cylindrical Extensions and Their Intersection14:56
Reasoning with Projections16:21
Using other Projections pt 120:01
Using other Projections pt 221:11
Is Decomposition Always Possible?21:41
Relational Graphical Models: Formalization25:23
Possibility-Based Formalization pt 125:25
A Tutorial on Graphical Models and How to Learn Them from Data (a)26:06
Possibility-Based Formalization pt 1 (a)26:58
Possibility-Based Formalization pt 228:41
Possibility-Based Formalization pt 330:36
Relational Decomposition: Simple Example32:23
Possibility-Based Formalization pt 3 (a)33:02
Possibility-Based Formalization pt 1 (b)33:14
Possibility-Based Formalization pt 3 (b)33:34
Conditional Possibility and Independence34:35
Conditional Independence: Simple Example37:00
Relational Evidence Propagation38:36
Relational Evidence Propagation, Step 138:54
Relational Evidence Propagation (a)39:16
Relational Evidence Propagation, Step 1 (a)39:32
Relational Evidence Propagation (b)39:34
Relational Evidence Propagation, Step 1 (continued)39:39
Relational Evidence Propagation, Step 239:42
A Simple Example: The Probabilistic Case39:52
A Probability Distribution40:05
Reasoning: Computing Conditional Probabilities41:58
A Probability Distribution (a)43:20
Reasoning: Computing Conditional Probabilities (a)43:28
Probabilistic Decomposition: Simple Example44:28
Reasoning with Projections47:15
Probabilistic Graphical Models: Formalization50:15
Probabilistic Decomposition50:17
Probabilistic Decomposition: Simple Example (a)51:21
Conditional Independence52:12
Probabilistic Decomposition (continued)53:25
Conditional Independence (a)54:02
Probabilistic Decomposition (continued) (a)54:16
Conditional Independence: An Example pt 154:48
Conditional Independence: An Example pt 257:38
Conditional Independence: An Example pt 357:52
Conditional Independence: An Example pt 1 (a)58:33
Conditional Independence: An Example pt 2 (a)58:47
Reasoning with Projections59:13
Probabilistic Evidence Propagation, Step 159:36
Probabilistic Evidence Propagation, Step 1 (continued)59:40
Probabilistic Evidence Propagation, Step 259:41
Graphical Models: The General Theory59:52
(Semi-)Graphoid Axioms01:00:18
Illustration of the (Semi-)Graphoid Axioms01:04:31
Separation in Graphs01:06:23
Separation in Directed Acyclic Graphs01:08:17
Conditional (In)Dependence Graphs01:10:35
Limitations of Graph Representations01:12:15
Markov Properties of Undirected Graphs01:14:33
Markov Properties of Directed Acyclic Graphs01:14:36
Equivalence of Markov Properties01:14:38
Undirected Graphs and Decompositions01:14:41