Word embedding is a useful approach to capture co-occurrence structures in a large corpus of text. In addition to the text data itself, we often have additional covariates associated with individual documents in the corpus---e.g. the demographic of the author, time and venue of publication, etc.---and we would like the embedding to naturally capture the information of the covariates. In this paper, we propose CoVeR, a new tensor decomposition model for vector embeddings with covariates. CoVeR jointly learns a base embedding for all the words as well as a weighted diagonal transformation to model how each covariate modifies the base embedding. To obtain the specific embedding for a particular author or venue, for example, we can then simply multiply the base embedding by the transformation matrix associated with that time or venue. The main advantages of our approach is data efficiency and interpretability of the covariate transformation matrix. Our experiments demonstrate that our joint model learns substantially better embeddings conditioned on each covariate compared to the standard approach of learning a separate embedding for each covariate using only the relevant subset of data, as well as other related methods. Furthermore, CoVeR encourages the embeddings to be "topic-aligned" in the sense that the dimensions have specific independent meanings. This allows our covariate-specific embeddings to be compared by topic, enabling downstream differential analysis. We empirically evaluate the benefits of our algorithm on several datasets, and demonstrate how it can be used to address many natural questions about the effects of covariates.

CoVeR是一种新的张量分解模型，可以有效地学习向量嵌入和其相关协变量，同时具有解释性，通过实验验证获得了很好的效果。

CoVeR：使用张量分解学习协变量特定的向量表示