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.

在计算社会科学的各种应用中，静态词嵌入广泛存在并为实际决策做出了贡献，然而，从词嵌入统计中得出的下游结论的统计不确定性评估一直是具有挑战性的。本文提出了一种方法，通过使用多元正态模型的解析近似来获得 GloVe（Pennington 等，2014）的近似、易于使用和可扩展的重建误差方差估计，GloVe 是最广泛使用的词嵌入模型之一。为了展示具有方差（GloVe-V）的嵌入的价值，我们说明了我们的方法如何使核心词嵌入任务中的原则性假设检验变得合理，例如在向量空间中比较不同词对之间的相似性，评估不同模型的性能，并使用不同的词列表分析语料库中的种族或性别偏见的相对程度。