Joint distribution

The restricted Boltzmann machine is described by a Boltzmann distribution

$$ \begin{align} P_{rbm}(\mathbf{x},\mathbf{h}) = \frac{1}{Z} e^{-\frac{1}{T_0}E(\mathbf{x},\mathbf{h})}, \tag{1} \end{align} $$

where \( Z \) is the normalization constant or partition function, defined as

$$ \begin{align} Z = \int \int e^{-\frac{1}{T_0}E(\mathbf{x},\mathbf{h})} d\mathbf{x} d\mathbf{h}. \tag{2} \end{align} $$

It is common to ignore \( T_0 \) by setting it to one.