#graph-separation

Question 1: Select all that apply

mediumAI-checkedProbabilistic & Graphical Models

A Gibbs distribution over $x_1, \ldots, x_5$ factorises as $p \propto \phi_{12}(x_1,x_2)\,\phi_{13}(x_1,x_3)\,\phi_{14}(x_1,x_4)\,\phi_{23}(x_2,x_3)\,\phi_{25}(x_2,x_5)\,\phi_{45}(x_4,x_5).$ Draw its undirected graph (one edge per pair of variables that share a factor). Which statements hold for every such distribution? Select all that apply.

The neighbours of $x_3$ are $\{x_1, x_2\}$ 1
The Markov blanket of $x_4$ is $\{x_1, x_5\}$ 2
$x_3 \perp x_4 \mid \{x_1, x_2\}$ 3
$x_2 \perp x_4 \mid x_1$ 4
$x_3 \perp x_5 \mid x_2$ 5

Timed test