Wavelet-based non-parametric HMM´s: theory and applications

In this paper, we propose a new algorithm for non-parametric estimation of hidden Markov models (HMM). The algorithm is based on a “wavelet-shrinkage” density estimator for the state-conditional probability density functions of the HMM´s. It operates in an iterative fashion, similar to the EM re-estimation formulae used for maximum likelihood estimation of parametric HMM. We apply the resulting algorithm to simple examples and show its convergence. The performance of the proposed method is also compared to classical non-parametric HMM estimation based on quantization of observations (“histograms”) and discrete HMM. The algorithm is finally applied to a voice activity detection (VAD) task and its performance is compared to that of the histogram and Gaussian HMM methods