Another varient is the RBM where the visible units are Gaussian while the hidden units remain binary:
$$ \begin{align*} E(\boldsymbol{x}, \boldsymbol{h},\boldsymbol{\Theta}) = \sum_i^M \frac{(x_i - a_i)^2}{2\sigma_i^2} - \sum_j^N b_j h_j - \sum_{i,j}^{M,N} \frac{x_i w_{ij} h_j}{\sigma_i^2}. \end{align*} $$This type of RBMs are useful when we model continuous data (i.e., we wish \( \boldsymbol{x} \) to be continuous). The paramater \( \sigma_i^2 \) is meant to represent a variance and is foten just set to one.