Variance-Reduced Stochastic Optimization for Efficient Inference of Hidden Markov Models
Journal of Computational and Graphical Statistics(2023)
摘要
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 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.
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