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Laboratoire d'InfoRmatique en Image et Systèmes d'information

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Laboratoire d'InfoRmatique en Image et Systèmes d'information
UMR 5205 CNRS / INSA Lyon / Université Claude Bernard Lyon 1 / Université Lumière Lyon 2 / École Centrale de Lyon
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Fei Zheng

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PhD student

Team Feature Extraction and Identification
 
Institution École Centrale de Lyon
Location Ecully (Ecole Centrale de Lyon)
 
E-mail fei.zheng at liris.cnrs.fr
Contact details Publications Thesis
 
Subject Learning and Smoothing in Switching Markov Models with Copulas
Abstract Switching Markov Models, also called Jump Markov Systems (JMS), are widely used in many fields such as target tracking, seismic signal processing and finance, since they can approach non-Gaussian non-linear systems. A considerable amount of related work studies linear JMS in which data restoration is achieved by Markov Chain Monte-Carlo (MCMC) methods. In this dissertation, we try to find alternative restoration solution for JMS to MCMC methods. The main contribution of our work includes two parts. Firstly, an algorithm of unsupervised restoration for a recent linear JMS known as Conditionally Gaussian Pairwise Markov Switching Model (CGPMSM) is proposed. This algorithm combines a parameter estimation method named DEM, which is based on the Expectation-Maximization (EM) principle applied twice sequentially, and an efficient approach for smoothing with estimated parameters. Secondly, we extend a specific sub-model of CGPMSM known as Conditionally Gaussian Observed Markov Switching Model (CGOMSM) to a more general one, named Generalized Conditionally Observed Markov Switching Model (GCOMSM) by introducing Copulas. Comparing to CGOMSM, the proposed GCOMSM adopts inherently more flexible distributions and non-linear structures, while optimal restoration is feasible. In addition, an identification method called GICE-LS based on the Generalized Iterative Conditional Estimation (GICE) and the Least-Square (LS) principles is proposed for GCOMSM to approximate any non-Gaussian non-linear systems from their sample data set. All proposed methods are tested by simulation. Moreover, the performance of GCOMSM is discussed by application on other generable non-Gaussian non-linear Markov models, for example, on stochastic volatility models which are of great importance in finance.
Advisor Stéphane Derrode

Last update : 2018-01-11 13:43:29