Basic Concepts in Bayesian Networks

  1. Definition: two components: DAG for structure, conditional probability distribution
  2. Other names or related concepts: belief network, probabilistic network, causal network, knowledge map, graphical model, decision network, influence diagram
  3. Factorization, node ordering, modularity
  4. Local Markov assumption: given parents, a node is independent of other non-descendants

Global Markov assumption: given Markov blanket, a node is independent of other nodes

  1. I-map & D-map: minimal I-map, perfect map
  2. D-separation, conditional independent

three canonical structures: sequential, common cause, common effects

tested by: Bayes ball algorithm, moralized graph without irrelevant variables

  1. Independence-equivalent, distribution-equivalent, causality-equivalent
  2. moralization
  3. edge direction induction rules
  4. Representation of conditional probability distribution

1) table

2) tree structure

3) noisy-or

4) neural networks

5) generalized linear model for continuous variables

  1. categories of reasoning with Bayesian networks

1) prediction

2) abduction

3) explaining away

  1. query type:

1) conditional probability,

2) most probable explanation (joint distribution of query variables and evidence)

3) Maximum a posterior (MAP) (conditional distribution of query variables given evidence)

  1. Exact inference methods

0) Naïve enumeration

1) variable elimination

2) belief propagation

3) Junction tree algorithm

  1. approximate inference

1) direct sampling methods

2) rejection sampling methods

3) likelihood sampling methods

4) importance sampling methods

5) Gibbs sampling

6) Metropolis sampling

7) Markov chain Monte Carlo methods

  1. parameter estimation with known structure
  2. structure learning with unknown structure

1) search-and-score-based methods

maximum likelihood, Bayesian information criterion, BDe score

K2, Hill-climbing, MCMC

2) constraint-based methods

IC-algorithm, CI-algorithm, PC-algorithm

3) Bayesian model averaging

  1. File format of Bayesian networks
  2. Classic examples

1) Sprinkler network

2) Burglar & Earthquake & alarm network

3) Asia network

4) Alarm Network

5) QMR_DT

6) CPC network

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