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.
翻译:我们提出了一个新奇的算法,用于在几何设置中学习隐藏的Markov模型(HMMs)的参数,观测在几何设置中得出里曼尼方形的值。特别是,我们提升了最近的第二阶刻算法,将非连带性的相关性纳入到一个更笼统的设置中,在里曼尼非正曲线的对称空间中进行观测,观察可能性是里曼尼亚高斯人。由此形成的算法,将分解算法纳入里曼尼高斯混合模型的估算算法中,然后进行一系列康夫克斯优化程序。我们通过实例表明,与现有学习者相比,学习者可以大大提高速度和数字准确性。