Reformulating the HMM as a Trajectory Model

We have shown that the HMM whose state output vector includes static and dynamic feature parameters can be reformulated as a trajectory model by imposing the explicit relationship between the static and dynamic features. The derived model, referred to as “trajectory HMM,” can alleviate the limitations of HMMs: i) constant statistics within an HMM state and ii) independence assumption of state output probabilities. In this paper, we first summarize the definition and the training algorithm. Then, to show that the trajectory HMM is a proper generative model, we derive a new algorithm for sampling from the trajectory model, and show the result of an illustrative experiment. A speech recognition experiment demonstrates the consistency between training and decoding criteria is essential: the model should not only be traind as a trajectory model but also be used as a trajectory model in decoding, even though the trajectory model has the same parameterization as the standard HMM.

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