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Communication Dans Un Congrès Année : 2022

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

Résumé

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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Dates et versions

hal-04270489 , version 1 (04-11-2023)

Identifiants

Citer

Berlin Chen, Cyrus Mostajeran, Salem Said. Geometric Learning of Hidden Markov Models via a Method of Moments Algorithm. International Conference on Bayesian and Maximum Entropy methods in Science and Engineering -MaxEnt 2022, Jul 2022, Paris, France. pp.10, ⟨10.3390/psf2022005010⟩. ⟨hal-04270489⟩
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