In this method we sample from the joint probability \( P_{rbm} (\mathbf{x}, \mathbf{h}) \) by way of a two step sampling process. We alternately update the visible and hidden units. New samples are generated according to the conditional probabilities \( P(x_i|\mathbf{h}) \) and \( P(h_j|\mathbf{x}) \) respectively and accepted with the probability of \( 1 \). While the the visible nodes are dependent on the hidden nodes and vice versa, the nodes are independent of other nodes within the same layer. This is due to there being no intra layer interactions in the restricted Boltzmann machine.
The conditional probabilities are often referred to as the activitation functions in the neural networks context due to their role in determining the node outputs. For the binary-binary RBM they are $$ \begin{align} P(h_j = 1 | \boldsymbol{x}) &= \frac{1}{1 + e^{-b_j - \sum_i x_i w_{ij}}} \tag{9}\\ P(x_i = 1 | \boldsymbol{h}) &= \frac{1}{1 + e^{-a_j - \sum_j h_j w_{ij}}}, \tag{10} \end{align} $$ where we recognize the logistic sigmoid function \( \sigma (x) = 1/(1+exp(-x)) \).