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arXiv · 2207.00818

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

Berlin Chen·Cyrus Mostajeran·Salem Said
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Abstract

We present a novel algorithm for learning the parameters of hidden Markov models (HMMs) in a geometric setting where the observations take values in Riemannian manifolds. In particular, we elevate a recent second-order method of moments algorithm that incorporates non-consecutive correlations to a more general setting where observations take place in a Riemannian symmetric space of non-positive curvature and the observation likelihoods are Riemannian Gaussians. The resulting algorithm decouples into a Riemannian Gaussian mixture model estimation algorithm followed by a sequence of convex optimization procedures. We demonstrate through examples that the learner can result in significantly improved speed and numerical accuracy compared to existing learners.

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BibTeXRIS

Berlin Chen, Cyrus Mostajeran, Salem Said. 2022-07-02. Geometric Learning of Hidden Markov Models via a Method of Moments Algorithm. https://doi.org/10.3390/psf2022005010

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