Pedro domingos

Dear Professor:

          I am a university student in China and study on MLN recently;

         

          I have a question as follow:

          The joint distribution represented by a Markov network is given by $$P(X=x) = \frac{1}{Z} \prod_k \phi_{k}(x_{\{k\}})\tag{2.1}$$ $$P(X=x) = \frac{1}{Z} exp\left(\sum_j w_jf_j(x)\right)\tag{2.2}$$

          The probability distribution over possible worlds x specified by the ground Markov network $M_{L, C}$ is given by $$P(X=x) = \frac{1}{Z} exp\left(\sum_i w_in_i(x)\right) = \frac{1}{Z}\prod_i \phi_{i}(x_{\{i\}})^{n_i(x)}\tag{2.3}$$

          The probability of a ground predicate $X_l$ when its Markov blanket $B_l$ is in state $b_l$ is $$P(X_l=x_l|B_l=b_l) = \frac{exp(\sum_{f_i \in F_l} w_if_i(X_l=x_l, B_l=b_l)))}{exp(\sum_{f_i \in F_l} w_if_i(X_l=0, B_l=b_l))+exp(\sum_{f_i \in F_l} w_if_i(X_l=1, B_l=b_l))}\tag{3.3}$$

　　　  

          I can't figure out how to derive equation(3.3) from equation(2.1) or equation(2.3), maybe equation(3.3) is a definition, not a derivation ??