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We present a novel algorithm for learning the parameters of hidden Markovmodels (HMMs) in a geometric setting where the observations take values inRiemannian manifolds. In particular, we elevate a recent second-order method ofmoments algorithm that incorporates non-consecutive correlations to a moregeneral setting where observations take place in a Riemannian symmetric spaceof non-positive curvature and the observation likelihoods are RiemannianGaussians. The resulting algorithm decouples into a Riemannian Gaussian mixturemodel estimation algorithm followed by a sequence of convex optimizationprocedures. We demonstrate through examples that the learner can result insignificantly improved speed and numerical accuracy compared to existinglearners.

Geometric Learning of Hidden Markov Models via a Method of Moments Algorithm