  Estimating the parameters of probabilistic models of language such as maxent
models and probabilistic neural models is computationally difficult since it
involves evaluating partition functions by summing over an entire vocabulary,
which may be millions of word types in size. Two closely related
strategies---noise contrastive estimation (Mnih and Teh, 2012; Mnih and
Kavukcuoglu, 2013; Vaswani et al., 2013) and negative sampling (Mikolov et al.,
2012; Goldberg and Levy, 2014)---have emerged as popular solutions to this
computational problem, but some confusion remains as to which is more
appropriate and when. This document explicates their relationships to each
other and to other estimation techniques. The analysis shows that, although
they are superficially similar, NCE is a general parameter estimation technique
that is asymptotically unbiased, while negative sampling is best understood as
a family of binary classification models that are useful for learning word
representations but not as a general-purpose estimator.
