Learning Hidden Markov Models with Hidden Markov Trees as Observation Distributions

Hidden Markov models have been found very useful for a wide range of applications in artificial intelligence. The wavelet transform arises as a new tool for signal and image analysis, with a special emphasis on nonlinearities and nonstationarities. However, learning models for wavelet coecients have been mainly based on fixed-length sequences. We propose a novel learning architecture for sequences analyzed on a short-term basis, but not assuming stationarity within each frame. Long-term dependencies are modeled with a hidden Markov model which, in each internal state, deals with the local dynamics in the wavelet domain using a hidden Markov tree. The training algorithms for all the parameters in the composite model are developed using the expectation-maximization framework. This novel learning architecture can be useful for a wide range of applications. We detail experiments with real data for speech recognition. In the results, recognition rates were better than the state of the art technologies for this task.