  Word embedding algorithms produce very reliable feature representations of
words that are used by neural network models across a constantly growing
multitude of NLP tasks. As such, it is imperative for NLP practitioners to
understand how their word representations are produced, and why they are so
impactful.
  The present work presents the Simple Embedder framework, generalizing the
state-of-the-art existing word embedding algorithms (including Word2vec (SGNS)
and GloVe) under the umbrella of generalized low rank models. We derive that
both of these algorithms attempt to produce embedding inner products that
approximate pointwise mutual information (PMI) statistics in the corpus. Once
cast as Simple Embedders, comparison of these models reveals that these
successful embedders all resemble a straightforward maximum likelihood estimate
(MLE) of the PMI parametrized by the inner product (between embeddings). This
MLE induces our proposed novel word embedding model, Hilbert-MLE, as the
canonical representative of the Simple Embedder framework.
  We empirically compare these algorithms with evaluations on 17 different
datasets. Hilbert-MLE consistently observes second-best performance on every
extrinsic evaluation (news classification, sentiment analysis, POS-tagging, and
supersense tagging), while the first-best model depends varying on the task.
Moreover, Hilbert-MLE consistently observes the least variance in results with
respect to the random initialization of the weights in bidirectional LSTMs. Our
empirical results demonstrate that Hilbert-MLE is a very consistent word
embedding algorithm that can be reliably integrated into existing NLP systems
to obtain high-quality results.
