论文标题
通过矩算法的方法对隐藏的马尔可夫模型的几何学习
Geometric Learning of Hidden Markov Models via a Method of Moments Algorithm
论文作者
论文摘要
我们提出了一种新的算法，用于在几何环境中学习隐藏马尔可夫模型（HMMS）的参数，其中观测值在Riemannian歧管中取值。特别是，我们提升了一种瞬间算法的二阶方法，该方法将非统一的相关性纳入了更通用的环境，在这种情况下，观测值在非阳性弧度的Riemannian对称空间中进行，观察结果是Riemannian Gaussians。所得算法将其分解为Riemannian高斯混合模型估计算法，然后是一系列凸优化程序。我们通过例子证明，与现有学习者相比，学习者可以显着提高速度和数值准确性。
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.
