Parameter learning in a hidden trajectory model

A computer-implemented method for utilizing a computer having a processor to train a model used in speech recognition, the method comprising:

• accessing, with the processor, cepstral observation data representing acoustic data from a speech signal;
• learning a plurality of residual mean vectors and a plurality of residual diagonal covariance matrices based on differences between the cepstral observation data and values produced from a predictor function;
• utilizing a likelihood function for the cepstral observation data to learn means and covariances for distributions of vocal tract resonances in the cepstral observation data, comprising learning a plurality of vocal tract resonance (VTR) mean vectors and a plurality of VTR covariance matrices based on the vocal tract resonances in the cepstral observation data, wherein learning a plurality of VTR covariance matrices comprises using a gradient ascent, the gradient ascent using a gradient of a function that includes a vector that is a function of a speech unit identity and a temporal order in an utterance, wherein a frame independent as approximation is used to learn at least some of the covariance matrices;
• generating, with the processor, a hidden trajectory model using the residual mean vectors, residual diagonal covariance matrices, VTR mean vectors and VTR covariance matrices;
• and
• outputting, with the processor, the hidden trajectory model to characterize a received speech signal to recognize speech in the received speech signal.

A computer-implemented method for performing steps with a computer having a processor, the method comprising:

• accessing, with the processor, cepstral observation data representing acoustic data from a speech signal;
• estimating mean and covariance parameters for distributions of a hidden trajectory model that gives a probability of a vocal tract resonance (VTR) trajectory, comprising using the cepstral observation data to solve a set of equations, with the processor, to estimate mean vectors and covariance matrices for the hidden trajectory model, the set of equations including a direct gradient ascent algorithm with a heuristically chosen positive constant applied to a gradient of a log-likelihood of a sequence of observed cepstral values in the cepstral observation data given a speech unit, wherein the gradient ascent algorithm uses a heuristically chosen positive constant to control a learning rate at each iteration of the gradient ascent algorithm;
• and
• outputting, with the processor, the hidden trajectory model to characterize a received speech signal to recognize speech in the received speech signal.