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11-Bayesian_Network_Intro.md

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Bayesian Network Representation

If IBE used, each of n variables we wish to represent can take on d possible values (it has a domain of size d), then our joint distribution table will have $d^n$ entries, exponential in the number of variables and quite impractical to store!

Bayes nets avoid this issue by taking advantage of the idea of conditional probability.

[!DEFINITION] Bayes Net

We formally define a Bayes Net as consisting of:

example:

Structure of Bayes Nets

Two rules for Bayes Net independences

  • Each node is conditionally independent of all its ancestor nodes (non-descendants) in the graph, given all of its parents.
  • Each node is conditionally independent of all other variables given its Markov blanket1.

[!HELP]

这两个规则即是利用了条件概率的局部性，帮助我们将判断一个事件所需要考虑的其他事件的数量大大减少。

link

Footnotes

  1. A variable’s Markov blanket consists of parents, children, children’s other parents. ↩