The statistical partition function (from Boltzmann I think) looks like
$\sum_\mathbf{u} e^{-E(\mathbf{u})}$
It's used in Boltzmann machines, for example:
$P(\mathbf{v}) = e^{-E(\mathbf{v})}/\sum_\mathbf{u} e^{-E(\mathbf{u})}$
Say I want to calculate the log, base e of the partition function:
$log_e(\sum_\mathbf{u} e^{-E(\mathbf{u})})$
but I don't want to calculate the energy of each state explicitly, because that would take too long with hundreds or thousands of nodes in a Boltzmann machine. The energy is given by the weights and states of the network:
$E(\mathbf{v}) = -\sum_i s^\mathbf{v}_i b_i -\sum_{i How can I efficiently do this without calculating each state explicitly? I think it has something to do with this, but I'm not quite connecting the dots yet.