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@nanmeng 2016-05-19T09:17:20.000000Z 字数 1603 阅读 769

Probabilistic Graphical Models(Stanford) - 3

Probabilistic_Graphical_Models


Week2 Probabilistic Graphical Models

1. Overview: Structured CPDs

Tabular Representations

PGM2_1
A more general CPD:
PGM2_2
Model types:
PGM2_3

Context-Specific Independence

PGM2_4

An example:
PGM2_5

  • when is false: is the same as and are not independent
  • when is true: we do not care about because is always true and are independent
  • when is false: which means that and are both false when we know one of them is false, then we already know the other is false and are independent.
  • when is true: we do not know which of and made is true.

2. Tree-Structured CPDs

Example:
PGM2_6

  • if , then the recruiter do not looks at letter, so is independent of .
  • if , the and are independent of like what shown in the tree structure.
  • if the and are independent of
  • if and for both value of , so the statement here has two cases: and so in both the cases, the statement is true.
    PGM2_77

An example of multiplexer: the choice variable determines the circumstance or another set of circumstance.
PGM2_8
Question:

PGM2_9

Analysis:

  • given observed , active the active trail of
  • if we know , which means that the arrow between and is disappear, while if we know the arrow between and is disappear(like what we shown below).
    PGM2_10

A tell us which of the variable , need to copy.
PGM2_11

Summary

PGM2_12

3. Independence of Causal Influence

Sometimes it's not the case that you depend on one only in certain contexts, and not in others. Really, you depend on all of them and all of them sort of contribute something to the probability of
PGM2_13

Sigmoid CPD

PGM2_14
An intuitive view:
PGM2_15
Choices:
PGM2_16

4. Continuous Variables

The (inside temperature) is the linear combination of (current temperature) and (outside temperature).
PGM2_17
PGM2_18

Linear Gaussian

PGM2_19
PGM2_20
PGM2_21

An example"
Pgm2_22

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