The popular skip-gram model induces word embeddings by exploiting the signal from word-context coocurrence. We offer a new interpretation of skip-gram based on exponential family PCA-a form of matrix factorization to generalize the skip-gram model to tensor factorization. In turn, this lets us train embeddings through richer higher-order coocurrences, e.g., triples that include positional information (to incorporate syntax) or morphological information (to share parameters across related words). We experiment on 40 languages and show our model improves upon skip-gram.