Restricted Boltzman Machines for Collaborative Filtering

能量模型

Energy-based probabilistic models define a probability distribution through an energy function:

$$p(x)=\frac{e^-E(x)}{Z}$$
Z is called the partition function:
$Z=\sum_x{e^{-E(x)}}\mbox{(to make $\sum_x{P(x)}=1$)}$

The energy function of Boltzmann machine is given by:

$$E(x)=-x^TUx-b^Tx$$
When include latent variable,the Boltzmann machine become more powerful,and the energy function becomes:
$$E(v,h)=-v^TRv-v^TWh-h^TSh-b^Tv-c^Th$$
Learning algorithms for Boltzmann machines are usually based on maximum likelihood.