Geometric Learning of Hidden Markov Models via a Method of Moments Algorithm
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.
Code (0)
등록된 구현이 없습니다.
Methods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
Hidden Markov Transformer for Simultaneous Machine Translation
Simultaneous machine translation (SiMT) outputs the target sequence while receiving the source sequence, and hence learning when to start translating each target token is the core challenge for SiMT task. However, it is …
Machine TranslationTranslationA Spectral Algorithm for Inference in Hidden Semi-Markov Models
Hidden semi-Markov models (HSMMs) are latent variable models which allow latent state persistence and can be viewed as a generalization of the popular hidden Markov models (HMMs). In this paper, we introduce a novel spec…
A Method of Moments for Mixture Models and Hidden Markov Models
Mixture models are a fundamental tool in applied statistics and machine learning for treating data taken from multiple subpopulations. The current practice for estimating the parameters of such models relies on local sea…
parameter estimationRegime Switching Bandits
We study a multi-armed bandit problem where the rewards exhibit regime switching. Specifically, the distributions of the random rewards generated from all arms are modulated by a common underlying state modeled as a fini…
Reinforcement LearningSublinear Regret for Learning POMDPs
We study the model-based undiscounted reinforcement learning for partially observable Markov decision processes (POMDPs). The oracle we consider is the optimal policy of the POMDP with a known environment in terms of the…
reinforcement-learningReinforcement Learning (RL)