Variance-Reduced Stochastic Optimization for Efficient Inference of Hidden Markov Models
提出一种结合部分E步和方差缩减随机优化的新算法，在不遍历整个数据集的情况下更新隐马尔可夫模型参数，通过仿真和虎鲸运动数据验证其收敛更快、计算时间更短且似然更高。
Hidden Markov models (HMMs) are popular models to identify a finite number of latent states from sequential data. However, fitting them to large data sets can be computationally demanding because most likelihood maximization techniques require iterating through the entire underlying data set for every parameter update. We propose a novel optimization algorithm that updates the parameters of an HMM without iterating through the entire data set. Namely, we combine a partial E step with variance-reduced stochastic optimization within the M step. We prove the algorithm converges under certain regularity conditions. We test our algorithm empirically using a simulation study as well as a case study of kinematic data collected using suction-cup attached biologgers from eight northern resident killer whales (Orcinus orca) off the western coast of Canada. In both, our algorithm converges in fewer epochs, with less computation time, and to regions of higher likelihood compared to standard numerical optimization techniques. Our algorithm allows practitioners to fit complicated HMMs to large time-series data sets more efficiently than existing baselines. Supplemental materials are available online.