A Proofs to theorems in the paper If we have a proposal distribution q(x) satisfying ∀x, f (x) = 1 ∧f (x) = 1 ⇒ q(x) = 0, then equation (16) can be further written as Sometimes, it's hard for us to compute normalized probability q.
to tackle this problem, consider selfnormalized importance sampling as an unbiased estimation (Owen, 2013), whereŵ i is the normalized version of w. for a relation r with currently m subrelations, we turn it to a new sub-relation with probability p = α α + n + 1 (19) or to the k th existing sub-relation with probability where n k is the size of k th existing sub-relation, n is the sum of the number of all sub-relationships of r, and α is a hyperparameter, in which case we use α = 1.