Modeling and Unsupervised Classification of Multivariate Hidden Markov Chains With Copulas

Abstract—Parametric modeling and estimation of non-Gaussian multidimensional probability density function is a difficult problem whose solution is required by many applications in signal and image processing. A lot of efforts have been devoted to escape the usual Gaussian assumption by developing perturbed Gaussian models such as Spherically Invariant Random Vectors (SIRVs). In this work, we introduce an alternative solution based on copulas that enables theoretically to represent any multivariate distribution. Estimation procedures are proposed for some mixtures of copula-based densities and are compared in the hidden Markov chain setting, in order to perform statistical unsupervised classification of signals or images. Useful copulas and SIRV for multivariate signal classification are particularly studied through experiments Index Terms—Copulas, EM algorithm, hidden Markov chains, hidden Markov models, inference for margins, maximum likelihood, multivariate modeling, spherically invariant random vector (SIRV), statistical classification. I

Repairable systems with dependent components: Stochastic process techniques and models

We consider three approaches to the modeling of systems with repairable components by a multivariate stochastic on-off process. First, we discuss the Palm calculus framework for stationary processes and its power in the derivation of general formulae for joint downtime statistics in the case of statisti- cally independent components. Second, a class of Generalized Semi-Markov (GSMP) models is proposed for incorporating both arbitrary component downtime distributions and statistical dependence of component failures. The case of two components is studied in detail. Third, we define the property referred to as weakened-by-failures for a system of repairable components, and prove that it implies association under fairly general conditions. We also give sufficient conditions for our GSMP models to possess this property

Deep Learning Using Havrda-Charvat Entropy for Classification of Pulmonary Optical Endomicroscopy

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