This content of roadmap follows Prof. Jordan's lectures/textbook.
Conditional Independence and Factorization
- Much of our early discussion focused on conditional independence in the context of directed graphical models (Bayes nets) and undirected graphical models (Markov random fields - MRFs)
- We can use the Bayes Ball algorithm to determine conditional independencies in Bayes nets.
- We can use simple reachability algorithms to determine conditional independencies in MRFs
- We briefly discussed factor graphs, which provide a more fine-grained representation of the independencies in a MRF
- The variable elimination algorithm is based on interchanging sums and products in the definitions of marginals or partition functions but can perform many redundant calculations.
- the sum product algorithm is a belief propagation algorithm based on dynamic programming. It has the advantage over naive variable elimination in that it reuses computations to compute marginals for all nodes in the graph
- junction trees generalize the the sum product algorithm to arbitrary graphs by grouping variables together into cliques such that the cliques form a tree.