Penalized logistic regression with HMM log-likelihood regressors for speech recognition

Hidden Markov models (HMMs) are powerful generative models for sequential data that have been used in automatic speech recognition for more than two decades. Despite their popularity, HMMs make inaccurate assumptions about speech signals, thereby limiting the achievable performance of the conventional speech recognizer. Penalized logistic regression (PLR) is a well-founded discriminative classifier with long roots in the history of statistics. Its classification performance is often compared with that of the popular support vector machine (SVM). However, for speech classification, only limited success with PLR has been reported, partially due to the difficulty with sequential data. In this paper, we present an elegant way of incorporating HMMs in the PLR framework. This leads to a powerful discriminative classifier that naturally handles sequential data. In this approach, speech classification is done using affine combinations of HMM log-likelihoods. We believe that such combinations of HMMs lead to a more accurate classifier than the conventional HMM-based classifier. Unlike similar approaches, we jointly estimate the HMM parameters and the PLR parameters using a single training criterion. The extension to continuous speech recognition is done via rescoring of N-best lists or lattices.