A Bayesian Alternative to Gain Adaptation in Autoregressive Hidden Markov Models

Models dealing directly with the raw acoustic speech signal are an alternative to conventional feature-based HMMs. A popular way to model the raw speech signal is by means of an autoregressive (AR) process. Being too simple to cope with the nonlinearity of the speech signal, the AR process is generally embedded into a more elaborate model, such as the switching autoregressive HMM (SAR-HMM). A fundamental issue faced by models based on AR processes is that they are very sensitive to variations in the amplitude of the signal. One way to overcome this limitation is to use Gain Adaptation to adjust the amplitude by maximising the likelihood of the observed signal. However, adjusting model parameters by maximising test likelihoods is fundamentally outside the framework of standard statistical approaches to machine learning, since this may lead to overfitting when the models are sufficiently flexible. We propose a statistically principled alternative based on an exact Bayesian procedure in which priors are explicitly defined on the parameters of the AR process. Explicitly, we present the Bayesian SAR-HMM and compare the performance of this model against the standard Gain-Adapted SAR-HMM on a single digit recognition task, showing the effectiveness of the approach and suggesting thereby a principled and straightforward solution to the issue of Gain Adaptation.