I am reading about Boltzmann machines and according the formulas the joint probability of the states of all units is $$ P(X = x) = \frac{1}{Z} e^{-\frac{1}{2T} \sum_i\sum_j {x_i x_j w_{ij}}} $$$$ Z = \sum_x e^{-\frac{1}{2T}\sum_i\sum_j x_i x_j w_{ij}} $$In thse formulas it is assumed that $ w_{ii} = 0$. However it is infeasible to calculate the quantity $Z$ directly. Therefore people use Gibbs sampling to sample different states. I don't understand how exactly the sampling is used to estimate probabilities.
Estimating probability using boltzmann machine
machine learning