The 7th International Symposium on Intelligent Data Analysis

Graphical Models

author: Christian Borgelt, European Center for Soft Computing

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.

Categories

Top: Computer Science: Machine Learning: Graphical Models

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*Slides*
0:00	A Tutorial on Graphical Models and How to Learn Them from Data
1:09	Overview
3:16	Graphical Models: Core Ideas and Notions
8:35	A Simple Example: The Relational Case
9:31	A Simple Example
11:26	The Reasoning Space
12:04	The Relation in the Reasoning Space
12:33	Reasoning
13:45	Prior Knowledge and Its Projections
14:56	Cylindrical Extensions and Their Intersection
16:21	Reasoning with Projections
20:01	Using other Projections pt 1
21:11	Using other Projections pt 2
21:41	Is Decomposition Always Possible?
25:23	Relational Graphical Models: Formalization
25:25	Possibility-Based Formalization pt 1
26:06	A Tutorial on Graphical Models and How to Learn Them from Data (a)
26:58	Possibility-Based Formalization pt 1 (a)
28:41	Possibility-Based Formalization pt 2
30:36	Possibility-Based Formalization pt 3
32:23	Relational Decomposition: Simple Example
33:02	Possibility-Based Formalization pt 3 (a)
33:14	Possibility-Based Formalization pt 1 (b)
33:34	Possibility-Based Formalization pt 3 (b)
34:35	Conditional Possibility and Independence
37:00	Conditional Independence: Simple Example
38:36	Relational Evidence Propagation
38:54	Relational Evidence Propagation, Step 1
39:16	Relational Evidence Propagation (a)
39:32	Relational Evidence Propagation, Step 1 (a)
39:34	Relational Evidence Propagation (b)
39:39	Relational Evidence Propagation, Step 1 (continued)
39:42	Relational Evidence Propagation, Step 2
39:52	A Simple Example: The Probabilistic Case
40:05	A Probability Distribution
41:58	Reasoning: Computing Conditional Probabilities
43:20	A Probability Distribution (a)
43:28	Reasoning: Computing Conditional Probabilities (a)
44:28	Probabilistic Decomposition: Simple Example
47:15	Reasoning with Projections
50:15	Probabilistic Graphical Models: Formalization
50:17	Probabilistic Decomposition
51:21	Probabilistic Decomposition: Simple Example (a)
52:12	Conditional Independence
53:25	Probabilistic Decomposition (continued)
54:02	Conditional Independence (a)
54:16	Probabilistic Decomposition (continued) (a)
54:48	Conditional Independence: An Example pt 1
57:38	Conditional Independence: An Example pt 2
57:52	Conditional Independence: An Example pt 3
58:33	Conditional Independence: An Example pt 1 (a)
58:47	Conditional Independence: An Example pt 2 (a)
59:13	Reasoning with Projections
59:36	Probabilistic Evidence Propagation, Step 1
59:40	Probabilistic Evidence Propagation, Step 1 (continued)
59:41	Probabilistic Evidence Propagation, Step 2
59:52	Graphical Models: The General Theory
60:18	(Semi-)Graphoid Axioms
64:31	Illustration of the (Semi-)Graphoid Axioms
66:23	Separation in Graphs
68:17	Separation in Directed Acyclic Graphs
70:35	Conditional (In)Dependence Graphs
72:15	Limitations of Graph Representations
74:33	Markov Properties of Undirected Graphs
74:36	Markov Properties of Directed Acyclic Graphs
74:38	Equivalence of Markov Properties
74:41	Undirected Graphs and Decompositions

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