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Statistical Inference for Hidden Markov Tree Models and Application to Wavelet Trees

Jean-Baptiste Durand 1 Paulo Gonçalves 1
1 IS2 - Statistical Inference for Industry and Health
Inria Grenoble - Rhône-Alpes, LBBE - Laboratoire de Biométrie et Biologie Evolutive - UMR 5558
Abstract : The hidden Markov tree model was introduced by Crouse, Nowak and Baraniuk (1998) for modeling non-independent, non-Gaussian wavelet transform coefficien- ts. In their article, they developed an inductive algorithm, called «upward-do- wnward» algorithm, for likelihood computation. They also introduced Expectatio- n Maximization algorithms for likelihood maximization. These algorithms are subject to the same numerical limitations as the «forward-backward» procedure for hidden Markov chains. In this report, we develop efficient variants of the «upward-downward» and EM algorithms, inspired by Devijver's «conditional forward-backward» recursion (1985). Thus, the inference algorithm- s limitations for hidden Markov trees are considerably reduced. Moreover, as the hidden states restoration problem has no known solution for hidden Markov trees, we present the MAP algorithm for this model. The interest of those algorithms is illustrated by an application to signal processing.
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https://hal.inria.fr/inria-00072339
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Submitted on : Tuesday, May 23, 2006 - 8:28:07 PM
Last modification on : Friday, September 11, 2020 - 6:10:04 PM
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Jean-Baptiste Durand, Paulo Gonçalves. Statistical Inference for Hidden Markov Tree Models and Application to Wavelet Trees. [Research Report] RR-4248, INRIA. 2001. ⟨inria-00072339⟩

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