A Dynamical System Approach to Continuous Speech Recognition

A DYNAMICAL SYSTEM APPROACH TO CONTINUOUS SPEECH RECOGNITION V.Digalaki~f J.R. Rohlieek~i M.Ostendor~ t Boston University 44 Cuminington St. Boston, MA 02215 ABSTRACT A dynamical system model is proposed for better represent- ing the spectral dynamics of speech for recognition. We assume that the observed feature vectors of a phone segment are the output of a stochastic linear dynamical system and consider two alternative assumptions regarding the relationship of the segment length and the evolution of the dynamics. Training is equivalent to the identification of a stochastic linear system, and we follow a nontraditional approach based on the Estlmate-Maximize algo- rithm. We evaluate this model on a phoneme classification task using the TIMIT database. INTRODUCTION A new direction in speech recognition via statistical meth- ods is to move from frame-based models, such as Hidden Markov Models (HMMs), to segment-based models that provide a better framework for modeling the dynamics of the speech production mechanism. The Stochastic Segment Model (SSM) is a joint model for a sequence of observa- tions, allowing explicit modeling of time correlation. Orig- inally in the SSM, a phoneme was modeled as a sequence of feature vectors that obeyed a multivariate Gaussian dis- tribution. The variable length of an observed phoneme was handled either by modeling a fixed-length transformation of the observations [6] or by assuming the observation was a partially observed sample of a trajectory represented by a fixed-length model [7]. In the first case, the maximum like- lihood estimates of the parameters can be obtained directly, but the Estimate-Maximize algorithm [2] may be required in the second case. Unfortunately, the joint Gaussian model suffers from es- timation problems, given the number of acoustic features and the analysis-frame rate that modern continuous speech recognizers use. Therefore, a more constrained assumption about the correlation structure must be made. In previ- ous work [3], we chose to constrain the model to a time- inhomogeneous Gauss-Markov process. Under the Gauss- Markov assumption, we were able to model well the time correlation of the first few cepstral coefficients, but the per- formance decreased when a larger number of features were BBN Inc. 10 Moulton St. Cambridge, MA 02138 used. We attribute the performance decrease to insufficient training data and the noisy nature of the cepstral coeffi- dents. In this work we deal with the problem of noisy ob- servations through a time-inhomogeneous dynamical system formalism, including observation noise in our model. Under the assumption that we model speech as a Gaus- sian process at the frame-rate level, a linear state-space dy- namical system can be used to parameterize the density of a segment of speech. This a natural generalization of our previous Gauss-Markov approach, with the addition of modeling error in the form of observation noise. We can make two different assumptions to address the time-variability issue: 1. Trajectory invariance (A1): There are underlying un- observed trajectories in state-space that basic units of speech follow. In the dynamical system formalism, this assumption translates to a fixed sequence of state transition matrices …

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