Exercise 10.1 - Marginalizing a node in a DGM

Answers

Since Figure 10.14.(a) implies:

\begin{aligned} p (A, B, C, D, E, F, X) & = \sum_{x} p (A, B, C, D, E, F, x) \\ = p (A) \cdot p (B) \cdot p (C) \cdot p (D) \sum_{x} p (x | A, B) \cdot p (E | C, x) \cdot p (F | x, D) \\ = p (A) \cdot p (B) \cdot p (C) \cdot p (D) \cdot f (A, B, C, D, E, F) . \end{aligned}

Thus the marginalized graph has to decompose in such a way with clique ${A, B, C, D, E, F} .$ One option is as follows:

Figure 1: Exercise 10.1.

The edge from $E$ to $F$ is necessary since the joint probability cannot be decomposed into $f (A, B, C, D, E) \cdot g (A, B, C, D, F)$ .

solour_lfq

2021-03-24 13:42