Learning hidden Markov models with hidden Markov trees as observation distributions

DIEGO MILONE; LEANDRO DI PERSIA

Mar del Plata

Simposio; Simposio argentino de Inteligencia Artificial (ASAI 2007); 2007

Sociedad Argentina de Informática

Hidden Markov models have been found very useful for a wide range of applications in machine learning. The wavelet transform arises as a new tool for signal and image analysis, with a special emphasis on nonlinearities and nonstationarities. Learning models for wavelet coefficients have been mainly based on fixed-length sequences, but many real applications require to model variable-length, very long or real-time sequences. In this paper, 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.