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Understanding continuous speech uttered by a random speaker in a random language and in a variable environment is a difficult problem for a machine. To take into account the context implies a broad knowledge of the world, and this has been the main source of difficulty in speech related research. Only by simplifying the problem – restricting the vocabulary, the speech domain, the way sentences are constructed, the number of speakers, and the language to be used, and controlling the environmental noise – has automatic speech recognition been possible. For modeling temporal dependencies or multi-modal distributions of “real-world” tasks, Hidden Markov Models (HMMs) are one of the most commonly used statistical models. Because of this, HMMs have become the standard solution for modeling acoustic information in the speech signal and thus for most current speech recognition systems. When putting HMMs into practice, however, there are some assumptions that make evaluation, learning and decoding feasible. Even if effective, these assumptions are known to be poor. Therefore, the development of new acoustic models that overcome traditional HMM restrictions is an active field of research in Automatic Speech Recognition (ASR). For instance, the independence and conditional-independence assumptions encoded in the acoustic models are not correct, potentially degrading classification performance. Adding dependencies through expert knowledge and hand tuning can improve models, but it is often not clear which dependencies should be included. Different approaches for overcoming HMM restrictions and for modeling time-domain dependencies will be presented in this chapter. For instance, an algorithm to find the beststate sequence of HSMMs (Hidden Semi-Markov Models) allows a more explicit modeling of context. Durations and trajectory modeling have also been on stage, leading to more recent work on the temporal evolution of the acoustic models. Augmented statistical models have been proposed by several authors as a systematic technique for modeling HMM additional dependencies, allowing the representation of highly complex distributions. These dependencies are thus incorporated in a systematic fashion, even if the price for this flexibility is high. Focusing on time and parameter independence assumptions, we will explain a method for introducing N-gram based augmented statistical models in detail. Two approaches are presented: the first one consists of overcoming the parameter independence assumption by modeling the dependence between the different acoustic parameters and mapping the input

Overcoming HMM Time and Parameter Independence Assumptions for ASR