Probabilistic Graphical Models(Stanford) - 3

Probabilistic_Graphical_Models

Week2 Probabilistic Graphical Models

1. Overview: Structured CPDs

Tabular Representations

A more general CPD:

Model types:

Context-Specific Independence

An example:

• when $y_2$ is false: $x$ is the same as $y_1$ $\Rightarrow$ $x$ and $y_1$ are not independent
• when $y_2$ is true: we do not care about $y_1$ because $x$ is always true $\Rightarrow$ $x$ and $y_1$ are independent
• when $x$ is false: which means that $y_1$ and $y_2$ are both false $\Rightarrow$ when we know one of them is false, then we already know the other is false $\Rightarrow$ $y_1$ and $y_2$ are independent.
• when $x$ is true: we do not know which of $y_1$ and $y_2$ made $x$ is true.

2. Tree-Structured CPDs

Example:

• if $a_1$, $s_1$ then the recruiter do not looks at letter, so $J$ is independent of $L$.
• if $a_1$, the $L$ and $S$ are independent of $J$ like what shown in the tree structure.
• if $a_0$ the $L$ and $S$ are independent of $J$
• if $s_1$ and for both value of $A$, so the statement here has two cases: $(J \perp_c L | s_1, a_0)$ and $(J \perp_c L | s_1, a_1)$ so in both the cases, the statement is true.
  

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

Question:

Analysis:

• given observed $J$, active the active trail of $L_1 \rightarrow J \leftarrow L_2$
• if we know $c_1$, which means that the arrow between $L_2$ and $J$ is disappear, while if we know $c_2$ the arrow between $L_1$ and $J$ is disappear(like what we shown below).
  

A tell us which of the variable $Z$, $Y$ need to copy.

Summary

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

Sigmoid CPD

An intuitive view:

Choices:

4. Continuous Variables

The $T'$(inside temperature) is the linear combination of $T$(current temperature) and $O$(outside temperature).

Linear Gaussian

An example"