  We present explicit classes of probability distributions that can be learned
by Restricted Boltzmann Machines (RBMs) depending on the number of units that
they contain, and which are representative for the expressive power of the
model. We use this to show that the maximal Kullback-Leibler divergence to the
RBM model with $n$ visible and $m$ hidden units is bounded from above by $n -
\left\lfloor \log(m+1) \right\rfloor -
\frac{m+1}{2^{\left\lfloor\log(m+1)\right\rfloor}} \approx (n -1) - \log(m+1)$.
In this way we can specify the number of hidden units that guarantees a
sufficiently rich model containing different classes of distributions and
respecting a given error tolerance.
