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Matrix Factorization (MF) is a common method for generating recommendations,where the proximity of entities like users or items in the embedded spaceindicates their similarity to one another. Though almost all applicationsimplicitly use a Euclidean embedding space to represent two entity types,recent work has suggested that a hyperbolic Poincar\'e ball may be more wellsuited to representing multiple entity types, and in particular, hierarchies.We describe a novel method to embed a hierarchy of related music entities inhyperbolic space. We also describe how a parametric empirical Bayes approachcan be used to estimate link reliability between entities in the hierarchy.Applying these methods together to build personalized playlists for users in adigital music service yielded a large and statistically significant increase inperformance during an A/B test, as compared to the Euclidean model.

Music Recommendations in Hyperbolic Space: An Application of Empirical Bayes and Hierarchical Poincar\'e Embeddings