approximate inference in graphical models — forward and rejection sampling, likelihood weighting, gibbs sampling and mcmc, and loopy belief propagation, with the trade-offs that decide which to reach for.
Probabilistic Graphical Models
a probabilistic graphical model is a marriage of graph theory and probability: the graph records which variables talk to each other directly, and that structure alone dictates how compactly a joint distribution can be stored, which independencies it must satisfy, and how expensive it is to reason with. one set of ideas — factors, elimination, message passing, sampling — then serves diagnosis networks, spam filters, speech recognisers, image denoisers and gene-regulation maps alike.
this section grew out of unsw’s comp9418 (advanced topics in statistical machine learning), which is taught from darwiche’s modeling and reasoning with bayesian networks. 𐃏
the pages
- bayesian networks — the directed language: cpts, the chain rule, d-separation and its valves, markov blankets, naive bayes and friends, gaussian networks, a word on causality.
- markov networks — the undirected language: gibbs distributions and the partition function, hammersley–clifford, factor graphs, energy minimisation, crfs.
- exact inference — factors and variable elimination, elimination orders and treewidth, the jointree algorithm, mpe and map queries.
- approximate inference — the sampling ladder from forward sampling to gibbs, and loopy belief propagation.
- markov chains and hidden markov models — sequence models: stationary distributions, forward and viterbi, particle filters, dbns and kalman.
- learning graphical models — mle and smoothing, em for missing data, chow–liu trees and score-based structure search.
reading order
the pages are written to be read in the order listed: representation first (directed, then undirected), then the inference stack (exact, then approximate), then time, then learning. each page closes with a curated results list — the statements worth being able to reproduce cold — and a typeset pdf for printing.
bayesian networks from first principles — the chain rule, conditional probability tables, d-separation and its valve intuition, markov blankets, i-maps, naive bayes classifiers and gaussian networks.
exact inference in graphical models — factors, variable elimination, elimination orders and treewidth, the jointree (junction tree) algorithm with message passing, and mpe/map queries.
learning bayesian networks from data — maximum-likelihood estimation of cpts, additive smoothing, handling missing data with expectation-maximisation, and structure learning from chow-liu trees to score-based search.
sequence models as graphical models — markov chains and stationary distributions, hidden markov models, the forward and viterbi algorithms on the state trellis, particle filtering, and dynamic bayesian networks.
undirected graphical models — gibbs distributions and the partition function, hammersley-clifford, factor graphs, energy minimisation and map-mrf, separation semantics, moralisation, and conditional random fields.
Backlinks (1)
1. Machine Learning /wiki/ml/
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subtrees
- probabilistic graphical models — bayesian and markov networks, inference, hmms, learning