Presentation
Probabilistic graphical models combine probabilistic methods (in particular, the Bayesian approach, joint and conditional probabilities) and graph theory methods. One models a situation by considering every random variable as the vertex of a graph. Edges of the graph will represent, depending on the situation, either dependance (in the probabilistic sense) or causality, or simply mutual influence. Calculating the joint distribution gets much easier when using the underlying graph structure. From observed values for some random variables we can infer distributions for the nonobserved ones. Also, by using the notion of utility, we obtain influence diagrams, allowing us to take optimal decisions.
Prerequisites
Probability and graph theory basics
Duration:
20h
Content
1. Probabilistic reasoning
Basic probability notions, random variables, distributions, joint distribution, marginalization, Bayes formula, independence, conditional independence, probabilistic inference
2. Graph theory
Definitions, acyclicity, topological ordering, acyclic oriented graph, Markov blanket, clique, covering tree, Kruskal algorithm
3. Bayesian networks
Belief networks, the sprinkler example, v-structure, information propagation in a Bayesian network, d-connection, d-separation, Markov equivalence, immorality
4. Probabilistic graphical models
Potential, Markov networks, Gibbs distribution, separation in a Markov network, global and local Markov properties, Markov random fields, Hammersley-Clifford theorem, chain graphs, factor graphs, I-map, D-map, perfect map
5. Inference in trees
Markov chain, message passing, stationary distribution
6. Tree junction algorithm
Hugin propagation, consistence, running intersection property, junction tree, chordal graphs, perfect elimination order, Tarjan triangulation algorithm, Densmore Duke, Shafer-Shenoy propagation
7. Decision
Expected utility, decision tree, influence diagram, decision potential, probability potential, utility potential, strong junction tree, Markov decision process, Bellman equation, infinite horizon process
Organization
Examination
2h written exam, without documents
Scheduled activities
- C1 (1h30) Cours 1
- PC/TP 1 (1h30) PC/TP 1
- C2 (1h30) Cours 2
- PC/TP2 (1h30) PC/TP 2
- C3 (1h30) Cours 3
- PC/TP3 (1h30) PC/TP 3
- C4 (1h30) Cours 4
- PC/TP4 (1h30) PC/TP 4
- C5 (1h30) Cours 5
- PC/TP5 (1h30) PC/TP 5
- C6 (1h30) Cours 6
- PC/TP6 (1h30) PC/TP 6
- Eval (2h) Évaluation
Team
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