Identifying Mixtures Of Bayesian Network Distributions
summary
Gives the first algorithm that identifies finite mixtures of Bayesian-network distributions beyond empty graphs by reducing to mixed PROD and then to mixed IID, recovering per-constituent parent-conditioned probabilities via repeated “runs”, alignment across runs, and a constructive Bayesian unzipping procedure. Requires at least 3k−3 nodes with disjoint Markov boundaries, binary observables and a zeta-informative separation; runtime and sample complexity scale roughly exponential in k and like Δ^2 (Δ = max degree) and the method is provably correct under those conditions.
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chapters (13)
- 0:00Intro
- 0:57Bayesian networks (Pearl 1985)
- 2:26Bayesian network The assignment to
- 2:41Some examples
- 6:29The setting More than learning not always possible
- 9:12Mixture models
- 11:31Conditions for identifiability
- 16:29Problems and reductions
- 19:23Reducing MixBND to MixProd
- 28:49A good colection of runs
- 30:41Constructing a good collection of runs
- 35:31Bayesian unzipping
- 39:42Beyond final remarks
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