What Hmms Can’t Do

Hidden Markov models (HMMs) are the predominant methodology for automatic speech recognition (ASR) systems. Ever since their inception, it has been said that HMMs are an inadequate statistical model for such purposes. Results over the years have shown, however, that HMM-based ASR performance continually improves given enough training data and engineering effort. In this paper, we argue that there are, in theory at least, no theoretical limitations to the class of probability distributions representable by HMMs. In search of a model to supersede the HMM for ASR, therefore, we should search for models with better parsimony, computational properties, noise insensitivity, and that better utilize high-level knowledge sources.