Representation and De-interleaving of Mixtures of Hidden Markov Processes

De-interleaving of the mixtures of Hidden Markov Processes (HMPs) generally depends on its representation model. Existing representation models consider Markov chain mixtures rather than hidden Markov, resulting in the lack of robustness to non-ideal situations such as observation noise or missing observations. Besides, de-interleaving methods utilize a search-based strategy, which is time-consuming. To address these issues, this paper proposes a novel representation model and corresponding de-interleaving methods for the mixtures of HMPs. At first, a generative model for representing the mixtures of HMPs is designed. Subsequently, the de-interleaving process is formulated as a posterior inference for the generative model. Secondly, an exact inference method is developed to maximize the likelihood of the complete data, and two approximate inference methods are developed to maximize the evidence lower bound by creating tractable structures. Then, a theoretical error probability lower bound is derived using the likelihood ratio test, and the algorithms are shown to get reasonably close to the bound. Finally, simulation results demonstrate that the proposed methods are highly effective and robust for non-ideal situations, outperforming baseline methods on simulated and real-life data.