#marginal-inference

Question 1: Short answer

hardAI-checkedProbabilistic & Graphical Models

The factor tree below defines $p(x_1, \ldots, x_5) \propto \phi_A(x_1)\,\phi_B(x_2)\,\phi_C(x_1, x_2, x_3)\,\phi_D(x_3, x_4)\,\phi_E(x_3, x_5)\,\phi_F(x_5)$ over binary variables, with $\phi_A = (2, 4)$ , $\phi_B = (4, 4)$ , $\phi_F = (1, 8)$ (values for $x = 0, 1$ ) and

$x_1 x_2 x_3$	000	100	010	110	001	101	011	111
$\phi_C$	4	2	2	6	2	6	6	4

$(x_3, x_4)$ or $(x_3, x_5)$	(0, 0)	(1, 0)	(0, 1)	(1, 1)
$\phi_D(x_3, x_4)$	8	2	2	6
$\phi_E(x_3, x_5)$	3	6	6	3

Use the sum-product algorithm with $x_1$ as the root. What is $p(x_1 = 1)$ ?

Factor tree: phi_A - x1 - phi_C; phi_C also connects to x2 (which connects to phi_B) and to x3; x3 connects to phi_D - x4 and to phi_E - x5 - phi_F.

Timed test