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

• URL: http://arxiv.org/abs/2207.00818v1
• Date: Sat, 2 Jul 2022 12:24:38 GMT
• Title: Geometric Learning of Hidden Markov Models via a Method of Moments Algorithm
• Authors: Berlin Chen, Cyrus Mostajeran, Salem Said
• Abstract summary: We present a novel algorithm for learning the parameters of hidden Markov models (HMMs) in a geometric setting. We demonstrate through examples that the learner can result in significantly improved speed and numerical accuracy compared to existing learners.
• Score: 11.338112397748619
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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