#pairwise-potentials

Question 1: Single choice

mediumAI-checkedProbabilistic & Graphical Models

Write $p(\mathbf{x}) \propto \exp\left(-\tfrac{1}{2}\mathbf{x}^\top A \mathbf{x} - \mathbf{b}^\top \mathbf{x}\right)$ , with $A$ symmetric, as a pairwise Markov network $\prod_{i \le j} \phi_{ij}(x_i, x_j)$ . What is the factor $\phi_{ij}(x_i, x_j)$ for $i < j$ ?

$\exp(-\tfrac{1}{2} a_{ij}\, x_i x_j)$ 1
$\exp(-a_{ij}\, x_i x_j - b_i x_i)$ 2
$\exp(-a_{ij}\, x_i x_j)$ 3
$\exp(-2 a_{ij}\, x_i x_j)$ 4

#pairwise-potentials

Timed test