Nonlinear Parametric Hidden Markov Models

In previous work [4], we extended the hidden Markov model (HMM) framework to incorporate a global parametric variation in the output probabilities of the states of the HMM. Development of the parametric HMM was motivated by the task of simultaneoiusly recognizing and interpreting gestures that exhibit meaningful variation. With standard HMMs, such global variation confounds the recognition process. In this paper we extend the parametric HMM approach to handle nonlinear (non-analytic) dependencies of the output distributions on the parameter of interest. We show a generalized expectation-maximization (GEM) algorithm for training the parametric HMM and a GEM algorithm to simultaneously recognize the gesture and estimate the value of the parameter. We present results on a pointing gesture, where the nonlinear approach permits the natural azimuth/elevation parameterization of pointing direction.