Graphical models
Draw which variables directly influence which, and a joint distribution over dozens of variables collapses into a product of small tables. Bayes nets and Markov random fields, reading independence off a graph, explaining away, factor graphs, and exact inference by variable elimination and belief propagation — and why loops make it hard.
60 min
After this lesson you can
- Write the joint distribution of a Bayes net as a product of conditional probability tables and count its parameters
- Decide conditional independence for chains, forks and colliders, and apply d-separation to small graphs
- Explain explaining away with numbers
- Write an undirected model as a normalised product of clique potentials, and convert either kind to a factor graph
- Compute a marginal by variable elimination and by sum-product belief propagation, and say why exact inference is hard on loopy graphs
In this lesson
- Why structure is the whole game
- Bayesian networks: a joint distribution as a product of small tables
- Reading independence off the graph
- Undirected models: Markov random fields
- Factor graphs: one language for both
- Exact inference, part 1: variable elimination
- Exact inference, part 2: belief propagation on trees
- Why loops are hard
- In code
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