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Separation of Mixed Hidden Markov Model Sources

机译：混合隐马尔可夫模型源的分离

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摘要

In this contribution, we consider the problem of source separation in the case of noisy instantaneous mixtures. In a previous work, sources have been modeled by a mixture of Gaus-sians leading to an hierarchical Bayesian model by considering the labels of the mixture as hidden variables. However, in that work, labels have been assumed to be i.i.d. We extend this modelization to incorporate a Markovian structure for the labels. This extension is important for practical applications which are abundant: unsupervised classification and segmentation, pattern recognition, speech signal processing,... In order to estimate the mixing matrix and the a priori model parameters, we consider observations as incomplete data. The missing data are sources and labels : sources are missing data for observations and labels are missing data for incomplete missing sources. This hierarchical modelization leads to specific restoration maximization type algorithms. Restoration step can be held in three different manners: (ⅰ) Complete likelihood is estimated by its conditional expectation. This leads to the EM (expectation-maximization) algorithm, (ⅱ ) Missing data are estimated by their maximum a posteriori. This leads to JMAP (Joint maximum a posteriori) algorithm, (ⅲ ) Missing data are sampled from their a posteriori distributions. This leads to the SEM (stochastic EM) algorithm. A Gibbs sampling scheme is implemented to generate missing data.
机译：在这一贡献中，我们考虑了在嘈杂的瞬时混合物情况下的源分离问题。在以前的工作中，通过将混合的标签视为隐藏变量，通过混合高斯混合模型来建立分层贝叶斯模型来对源进行建模。但是，在这项工作中，标签被假定为i.i.d。我们扩展了这种模型化，为标签合并了马尔可夫结构。此扩展对于大量的实际应用很重要：无监督的分类和分段，模式识别，语音信号处理等。为了估计混合矩阵和先验模型参数，我们将观察值视为不完整的数据。缺少的数据是来源和标签：来源的数据是观察数据的缺失，标签是数据的不完整来源的缺失。这种分层建模导致了特定的恢复最大化类型算法。可以用三种不同的方式进行恢复步骤：（ⅰ）完全似然是通过其条件期望来估计的。这导致了EM（期望最大化）算法，（ⅱ）丢失的数据是通过它们的最大后验来估计的。这导致了JMAP（联合最大后验）算法，（ⅲ）从后验分布中采样丢失的数据。这导致了SEM（随机EM）算法。实施吉布斯采样方案以生成丢失的数据。

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