Sparse regression has recently been applied to enable transfer learning from very limited data. We study an extension of this approach to unsupervised learning---in particular, learning word embeddings from unstructured text corpora using low-rank matrix factorization. Intuitively, when transferring word embeddings to a new domain, we expect that the embeddings change for only a small number of words---e.g., the ones with novel meanings in that domain. We propose a novel group-sparse penalty that exploits this sparsity to perform transfer learning when there is very little text data available in the target domain---e.g., a single article of text. We prove generalization bounds for our algorithm. Furthermore, we empirically evaluate its effectiveness, both in terms of prediction accuracy in downstream tasks as well as in terms of interpretability of the results.