We propose a new framework and the associated maximum-likelihood and discriminative training algorithms for the variable-parameter hidden Markov model (VPHMM) whose mean and variance parameters vary as functions of additional environment-dependent conditioning parameters. Our framework differs from the VPHMM proposed by Cui and Gong (2007) in that piecewise spline interpolation instead of global polynomial regression is used to represent the dependency of the HMM parameters on the conditioning parameters, and a more effective functional form is used to model the variances. Our framework unifies and extends the conventional discrete VPHMM. It no longer requires quantization in estimating the model parameters and can support both parameter sharing and instantaneous conditioning parameters naturally. We investigate the strengths and weaknesses of the model on the Aurora-3 corpus. We show that under the well-matched condition the proposed discriminatively trained VPHMM outperforms the conventional HMM trained in the same way with relative word error rate (WER) reduction of 19% and 15%, respectively, when only mean is updated and when both mean and variances are updated.
Index Terms—Discriminative training, growth transformation, parameter clustering, speech recognition, spline interpolation, variable-parameter hidden Markov model (VPHMM).