P (w|v) represents the probability of translating word v into word w. P (w|v) is heuristically calculated as where sim(w, v) is the word similarity between w and v. In order to calculate P (w|v), cosine distances between pre-trained word embeddings were recently utilized (Zuccon et al., 2015;Ganguly et al., 2015).
the word similarity is calculated as where w is the word embedding normalized to a unit length for w. This paper proposes a novel probabilistic IR method based on hyperspherical QLM that leverages pre-trained word embeddings as random variables for directional probabilistic models.