Asma MEDDEB, Souad CHEBBI, Nesrine AMOR, Sahbi MARROUCHI

A comparative study of nonlinear Bayesian filtering algorithms for estimation of gene expression time series data

This paper addresses the problem of estimating the time series of a gene expression using nonlinear Bayesianfiltering algorithms. The response of gene regulatory networks (GRNs) to functional requirements in the cell andenvironmental conditions evolves over time. Dynamic biological processes such as cancer progression and treatmentrecovery depend on the collected genetic profiles. These processes are behind genetic interactions that rewire overthe course of time. The GRN was formulated as a nonlinear and non-Gaussian dynamic system defined by the genemeasurement model and the unknown state is an evolution of the gene model. However, the GRN has a high dimensionalspace where most of nonlinear Bayesian filtering algorithms are ineffective in high dimensional spaces. Therefore, manyauthors have introduced various techniques to overcome what has become known as the curse of dimensionality. Thispaper presents a comparative study between extended Kalman filter, unscented Kalman filter and derivatives of particlefilters, in tracking the evolution of gene expression over time. Application of the nonlinear Bayesian filtering algorithmsto estimate the evolution of gene expression from synthetic and real data, shows that the unscented particle filter (UKFPF) provides promising and robust results compared to other filters. Furthermore, UKF-PF provides an alternativesolution to the problem of modeling gene regulatory networks.

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