  Static word embeddings are ubiquitous in computational social science
applications and contribute to practical decision-making in a variety of fields
including law and healthcare. However, assessing the statistical uncertainty in
downstream conclusions drawn from word embedding statistics has remained
challenging. When using only point estimates for embeddings, researchers have
no streamlined way of assessing the degree to which their model selection
criteria or scientific conclusions are subject to noise due to sparsity in the
underlying data used to generate the embeddings. We introduce a method to
obtain approximate, easy-to-use, and scalable reconstruction error variance
estimates for GloVe (Pennington et al., 2014), one of the most widely used word
embedding models, using an analytical approximation to a multivariate normal
model. To demonstrate the value of embeddings with variance (GloVe-V), we
illustrate how our approach enables principled hypothesis testing in core word
embedding tasks, such as comparing the similarity between different word pairs
in vector space, assessing the performance of different models, and analyzing
the relative degree of ethnic or gender bias in a corpus using different word
lists.
