Index: Friedman 2000 - Being Bayesian about Network Structure

Friedman 2000 - Being Bayesian about Network Structure

Routing Summary

Full capture of Friedman and Koller (UAI 2000; arXiv:1301.3856), Being Bayesian about Network Structure: feature posteriors for Bayesian network structure via closed-form sums for a fixed ordering and MCMC over orderings. (Journal version: Machine Learning 2003; conference version used here.)

• Need the paper on one page, PyMC example E20, section map? → Friedman 2000 - Being Bayesian about Network Structure - Overview
• Need priors, modularity, Theorem 2.1, why averaging is hard? → Friedman 2000 - Bayesian Structure Learning Framework
• Need eq. 6, edge and Markov-blanket posteriors? → Friedman 2000 - Closed Form for a Known Ordering
• Need order-MCMC and tricks? → Friedman 2000 - MCMC over Orderings and Computational Tricks
• Need experiments (Flare, Vote, Alarm, bootstrap)? → Friedman 2000 - Experiments Mixing and Feature Recovery
• Need BGe, Sachs interventions, Gaussian graphical models? → Bayesian Causal Discovery - BGe Score, Interventions and Sachs Data

Concept Map

Concept	Note	Type	Depends On	Key Result
Feature posterior, modularity	Friedman 2000 - Bayesian Structure Learning Framework	definition	none	$P(D\mid G)=\prod \text{score}$
Sum over DAGs given ordering	Friedman 2000 - Closed Form for a Known Ordering	theorem	framework	cost $n^{k+1}$
Order-MCMC	Friedman 2000 - MCMC over Orderings and Computational Tricks	theorem	closed form	flip and cut proposals
Experiments	Friedman 2000 - Experiments Mixing and Feature Recovery	example	order-MCMC	faster mixing than structure-MCMC

Notes

• Friedman 2000 - Being Bayesian about Network Structure - Overview — CONTAINS: question, contributions, E20 link, Source Map.
• Friedman 2000 - Bayesian Structure Learning Framework — CONTAINS: eq. 1-4, priors, Thm 2.1, why averaging is hard.
• Friedman 2000 - Closed Form for a Known Ordering — CONTAINS: eq. 5-8, Prop. 3.1-3.2, verification code.
• Friedman 2000 - MCMC over Orderings and Computational Tricks — CONTAINS: order-MCMC, four tricks, code skeleton.
• Friedman 2000 - Experiments Mixing and Feature Recovery — CONTAINS: Flare/Vote/Alarm results, Figs. 1-7, discussion.

Sources

Friedman 2000 - Being Bayesian about Network Structure (arXiv:1301.3856).

See Also

Causal Discovery - Overview | GES and Score-Based Discovery | PC Algorithm and Constraint-Based Discovery