#gibbs-sampling

Question 1: Single choice

mediumAI-checkedProbabilistic & Graphical Models

A restricted Boltzmann machine over binary visibles $\mathbf{v}$ and hiddens $\mathbf{h}$ has $p(\mathbf{v}, \mathbf{h}) \propto \exp(\mathbf{v}^\top W \mathbf{h} + \mathbf{a}^\top\mathbf{v} + \mathbf{b}^\top\mathbf{h})$ . Its conditionals factorise: $p(h_i = 1 \mid \mathbf{v}) = \sigma(\sum_j v_j W_{ji} + b_i)$ and $p(v_i = 1 \mid \mathbf{h}) = \sigma(\sum_j W_{ij} h_j + a_i)$ . How do you generate (approximate) samples from $p(\mathbf{v})$ ?

Sample each $v_i$ independently from its marginal $p(v_i)$ 1
Compute $p(\mathbf{v})$ exactly by summing over $\mathbf{h}$ , then sample from it2
Block Gibbs: alternately sample all $h_i$ given $\mathbf{v}$ and all $v_i$ given $\mathbf{h}$ 3
Sample $\mathbf{h}$ from its marginal $p(\mathbf{h})$ , then $\mathbf{v}$ given $\mathbf{h}$ 4

Timed test