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We present a framework for building unsupervised representations of entitiesand their compositions, where each entity is viewed as a probabilitydistribution rather than a vector embedding. In particular, this distributionis supported over the contexts which co-occur with the entity and are embeddedin a suitable low-dimensional space. This enables us to consider representationlearning from the perspective of Optimal Transport and take advantage of itstools such as Wasserstein distance and barycenters. We elaborate how the methodcan be applied for obtaining unsupervised representations of text andillustrate the performance (quantitatively as well as qualitatively) on taskssuch as measuring sentence similarity, word entailment and similarity, where weempirically observe significant gains (e.g., 4.1% relative improvement overSent2vec, GenSen).  The key benefits of the proposed approach include: (a) capturing uncertaintyand polysemy via modeling the entities as distributions, (b) utilizing theunderlying geometry of the particular task (with the ground cost), (c)simultaneously providing interpretability with the notion of optimal transportbetween contexts and (d) easy applicability on top of existing point embeddingmethods. The code, as well as prebuilt histograms, are available underhttps://github.com/context-mover/.

Context Mover's Distance & Barycenters: Optimal Transport of Contexts for Building Representations