For incorporating it in VINCULUM, we seek a document-wise assignment of entity links that maximizes the sum of the coherence scores between each pair of entity links predicted in the document d, i.e.
where φ is a function that measures the coherence between two entities, M for a mention m and each of its candidates, we compute a score, coh(c) = Since both measures take values between 0 and 1, we denote the coherence score coh(c) as p φ (c|P d ), the conditional probability of an entity given other entities in the document.