#hammersley-clifford

Question 1: Single choice

mediumAI-checkedProbabilistic & Graphical Models

A positive pmf $p(x_1, \ldots, x_4, y_1, \ldots, y_4)$ has the Markov blankets $\mathrm{MB}(x_1) = \{x_2, y_1\}$ , $\mathrm{MB}(x_2) = \{x_1, x_3, y_2\}$ , $\mathrm{MB}(x_3) = \{x_2, x_4, y_3\}$ , $\mathrm{MB}(x_4) = \{x_3, y_4\}$ and $\mathrm{MB}(y_i) = \{x_i\}$ for $i = 1, \ldots, 4$ . Which factorisation over the maximal cliques of the corresponding undirected graph does $p$ have?

$\frac{1}{Z}\prod_{i=1}^{4} g_i(x_i, y_i)$ 1
$\frac{1}{Z}\, g(y_1, \ldots, y_4) \prod_{i=1}^{3} m_i(x_i, x_{i+1}) \prod_{i=1}^{4} g_i(x_i, y_i)$ 2
$\frac{1}{Z}\prod_{i=1}^{3} m_i(x_i, x_{i+1}) \prod_{i=1}^{4} g_i(x_i, y_i)$ 3
$\frac{1}{Z}\prod_{i=1}^{3} m_i(x_i, x_{i+1}, y_i)\; g_4(x_4, y_4)$ 4

#hammersley-clifford

Timed test