弥合可用性差距：隐马尔可夫模型谱学习的理论和方法进展
Bridging the Usability Gap: Theoretical and Methodological Advances for Spectral Learning of Hidden Markov Models
AI总结：
针对隐马尔可夫模型谱学习（SHMM）的误差传播与渐近理论缺失问题，提出了投影SHMM（PSHMM）算法及在线学习变体，有效提升了估计与预测的稳健性。
摘要：
Baum-Welch (B-W) 算法是推断隐马尔可夫模型 (HMM) 最广受接受的方法。然而，它容易陷入局部最优，且对于许多实时应用而言可能太慢。文献中已提出基于矩方法 (MOM) 的 HMM 谱学习 (SHMM) 来克服这些障碍。尽管前景广阔，但 SHMM 的渐近理论一直难以捉摸，且由于不受控制的误差传播，SHMM 的长期性能可能会下降。在本文中，我们 (1) 提供了 SHMM 估计的似然近似误差的渐近分布，(2) 提出了一种名为投影 SHMM (PSHMM) 的新颖算法，以缓解误差传播问题，以及 (3) 开发了 SHMM 和 PSHMM 的在线学习变体，以适应潜在的非平稳性。我们在模拟数据和真实世界应用的数据上比较了 SHMM 与 PSHMM 的性能以及通过 B-W 算法的估计，发现 PSHMM 不仅保留了 SHMM 的计算优势，还提供了更稳健的估计和预测。
英文摘要：
The Baum-Welch (B-W) algorithm is the most widely accepted method for inferring hidden Markov models (HMM). However, it is prone to getting stuck in local optima, and can be too slow for many real-time applications. Spectral learning of HMMs (SHMM), based on the method of moments (MOM) has been proposed in the literature to overcome these obstacles. Despite its promises, asymptotic theory for SHMM has been elusive, and the long-run performance of SHMM can degrade due to unchecked propagation of error. In this paper, we (1) provide an asymptotic distribution for the approximate error of the likelihood estimated by SHMM, (2) propose a novel algorithm called projected SHMM (PSHMM) that mitigates the problem of error propagation, and (3) develop online learning variants of both SHMM and PSHMM that accommodate potential nonstationarity. We compare the performance of SHMM with PSHMM and estimation through the B-W algorithm on both simulated data and data from real world applications, and find that PSHMM not only retains the computational advantages of SHMM, but also provides more robust estimation and forecasting.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
