Assume a simplified version of our model, where a small window of k words is generated as follows: sample c ∼ C, where C is a uniformly random unit vector, then sample Furthermore, assume Z c = Z for any c. Lemma 3.1.
in the simplified version of our model, the Maximum-a-Posteriori (MAP) estimate of c using the MAP estimate of c t gives essentially the same expression as CBOW apart from the rescaling, which is often omitted due to computational efficiency in empirical works.