Spectral Learning of Hidden Markov Models with Group Persistence
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چکیده
In this paper, we develop a general Method of Moments (MoM) based parameter estimation framework for Switching Hidden Markov Model (SHMM) variants. The main obstacle for deriving a straightforward MoM algorithm for these models is the inherent permutation ambiguity in the parameter estimation, which causes the parameters of individual HMM groups to get mixed. We show that, as long as a global transition matrix has a group persistence property, it is possible to isolate the group parameters using a spectral de-permutation approach. We also provide a noise bound on the eigenvalues of the recovered transition matrix. We do experiments on synthetic data which shows the accuracy and the computational advantage of the proposed approach. We also perform a segmentation experiment on saxophone note sequences.
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