PASCAL Bootcamp in Machine Learning, Marseille 2010

Graphical Models

author: Cedric Archambeau, University College London
published: Aug. 5, 2010, recorded: July 2010, views: 685

Slides

Slides
0:00	An Introduction to Probabilistic Graphical Models
0:23	Reference material
2:26	Statistical machine learning: A mariage between statistics and computer science
5:12	Graphical models: A marriage between probability theory and graph theory
7:38	Graphical models are applied in ...
8:28	Organising document collections (Blei et al., JMLR 2003)
12:19	Bioinformatics (Husmeier et al.)
13:48	Image denoising (McAuley et al., ICML 2006)
15:29	Printer infrastructure management
17:05	Overview (1)
18:40	Basics
21:13	Conditional independence (CI)
24:54	CI examples
25:45	Probabilistic graphical model
28:10	Overview (2)
28:34	Bayesian networks (directed graphical models)
31:13	Factorisation in directed graphical models (1)
32:20	Bayesian networks (directed graphical models)
32:22	Factorisation in directed graphical models (1)
32:24	Bayesian networks (directed graphical models)
32:27	Factorisation in directed graphical models (1)
32:33	Bayesian networks (directed graphical models)
32:46	Factorisation in directed graphical models (1)
35:32	Factorisation in directed graphical models (2)
39:49	D-separation
41:55	Head-to-tail nodes: independence
45:49	Head-to-tail nodes: conditional independence
47:31	Head-to-tail nodes: independence
48:24	Bayesian networks (directed graphical models)
48:34	Tail-to-tail nodes: independence
50:34	Tail-to-tail nodes: conditional independence
51:24	Head-to-head nodes: independence
52:38	Head-to-head nodes: conditional independence
52:52	Blocked paths
55:17	D-separation, CI and factorisation
58:49	Markov blanket in Bayesian networks
62:28	Head-to-head nodes: independence
62:43	Markov blanket in Bayesian networks
62:54	Overview (3)
63:19	Markov random elds (undirected graphical models)
65:24	Graph separation
68:20	Cliques
69:30	Factorisation in undirected graphical models
73:31	Separation, CI and factorisation
75:54	MRFs versus Bayesian networks
79:14	Mapping a Bayesian networks into a MRF
82:02	Overview (4)
83:14	Exact inference in graphical models
86:55	Graphical interpretation of Bayes' rule
89:53	Belief propagation in a (Markov) chain (1)
93:48	Belief propagation in a (Markov) chain (2)
94:18	Belief propagation in a (Markov) chain (1)
94:28	Belief propagation in a (Markov) chain (2)
94:31	Belief propagation in a (Markov) chain (1)
94:43	Belief propagation in a (Markov) chain (2)
96:18	Belief propagation in a (Markov) chain (1)
96:41	Belief propagation in a (Markov) chain (2)
97:14	Belief propagation in a (Markov) chain (1)
97:40	Belief propagation in a (Markov) chain (2)
97:52	Belief propagation in a tree

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Description

We will discuss probabilistic graphical models associated to directed and undirected graphs. We will introduce exact inference algorithms, such as the sum-product algorithm, and apply it to hidden Markov models. We will also discuss elements of learning in graphical models including maximum likelihood, maximum a posteriori and the expectation-maximisation algorithm.