Geometric Learning of Hidden Markov Models via a Method of Moments Algorithm
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Abstract (arXiv)
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.
Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 11 of its 33 references that are in the map. First posted on arXiv 2 Jul 2022.
Builds on
11 of 33 references.
References · 11
- 2017Poincar'e Embeddings for Learning Hierarchical Representationscited by 674
- 2013Manopt, a Matlab toolbox for optimization on manifoldscited by 112
- 2018geomstats: a Python Package for Riemannian Geometry in Machine Learningcited by 71
- 2016Partially Observed Markov Decision Processes. Problem Sets and Internet Supplementcited by 34
- 2013On learning parametric-output HMMscited by 5
- 2018Learning Hidden Markov Models from Pairwise Co-occurrences with Application to Topic Modelingcited by 4
- 2019Geometric Matrix Midrangescited by 3
- 2020Inductive Geometric Matrix Midrangescited by 3
- 2020Riemannian Gaussian distributions, random matrix ensembles and diffusion kernelscited by 3
- 2021Online learning of Riemannian hidden Markov models in homogeneous Hadamard spacescited by 3
- 2017Asymptotically Efficient Identification of Known-Sensor Hidden Markov Modelscited by 1
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Citing papers per year: 2023: 2.
2 papers.