Hidden semi-Markov models (HSMMs) are latent variable models which allowlatent state persistence and can be viewed as a generalization of the popularhidden Markov models (HMMs). In this paper, we introduce a novel spectralalgorithm to perform inference in HSMMs. Unlike expectation maximization (EM),our approach correctly estimates the probability of given observation sequencebased on a set of training sequences. Our approach is based on estimatingmoments from the sample, whose number of dimensions depends onlylogarithmically on the maximum length of the hidden state persistence.Moreover, the algorithm requires only a few matrix inversions and is thereforecomputationally efficient. Empirical evaluations on synthetic and real datademonstrate the advantage of the algorithm over EM in terms of speed andaccuracy, especially for large datasets.
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