Word Embeddings as Statistical Estimators

Word embeddings are a fundamental tool in natural language processing. Currently, word embedding methods are evaluated on the basis of empirical performance on benchmark data sets, and there is a lack of rigorous understanding of their theoretical properties. This paper studies word embeddings from a statistical theoretical perspective, which is essential for formal inference and uncertainty quantification. We propose a copula-based statistical model for text data and show that under this model, the now-classical Word2Vec method can be interpreted as a statistical estimation method for estimating the theoretical pointwise mutual information (PMI). We further illustrate the utility of this statistical model by using it to develop a missing value-based estimator as a statistically tractable and interpretable alternative to the Word2Vec approach. The estimation error of this estimator is comparable to Word2Vec and improves upon the truncation-based method proposed by Levy and Goldberg (Adv. Neural Inf. Process. Syst., 27, 2177-2185 2014). The resulting estimator also is comparable to Word2Vec in a benchmark sentiment analysis task on the IMDb Movie Reviews data set and a part-of-speech tagging task on the OntoNotes data set.