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# Hyperbolic Manifold Regression

*Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics*, PMLR 108:2570-2580, 2020.

#### Abstract

Geometric representation learning has shown great promise for important tasks inartificial intelligence and machine learning. However, an open problem is yethow to integrate non-Euclidean representations with standard machine learningmethods.In this work, we consider the task of regression onto hyperbolic space for whichwe propose two approaches: a non-parametric kernel-method for which we also proveexcess risk bounds and a parametric deep learning model that is informed bythe geodesics of the target space.By recasting predictions on trees as manifold regression problems we demonstrate the applications of our approach on two challenging tasks: 1)hierarchical classification via label embeddings and 2) inventing new conceptsby predicting their embedding in a continuous representation of a base taxonomy.In our experiments, we find that the proposed estimators outperform their naivecounterparts that perform regression in the ambient Euclidean space.