Abstract

We have stayed too long with traditional input-output system models. The nature of modern data is different: they involve two-way interacting variables in large quantities. MIMO models provide only a partial solution and network modelling seems to be the way forward for dealing with data now vastly available in various applications ranging from social networks to finance and from genomics to mobile communications. Despite the explosion of research on big data, the time varying dimension of the interactions are widely ignored. In this talk, we address the problem of time varying network estimation with gene interaction networks as a case study.

Existing methods used for gene regulatory network identification are mostly dedicated to inference of steady state networks which are prevalent over all time instants. However, the interactions among genes in a network are not stationary during the life cycle of an organism. Moreover, information about the gene interactions in different stages of a life cycle is of high importance for biology in understanding of protein production, human diseases and in designing personalized treatment plans. In the literature one can find a large amount of data measured at a single time instant. Unfortunately, only a limited amount of sources present experimental data on temporal sequences for gene expression and most of available experimental data are measured sparsely or/and for a short time period. This lack of experimental data significantly limits the success of inference on network topology. We model the gene interactions over time with multivariate linear regressions where the parameters of the regressive process are changing over time. We propose Particle Filtering for dynamic network inference and its potentials in time varying gene expression tracking are demonstrated. The proposed model is able to track the interactions not only from the one step past but also interactions with a delay of n-time steps which is a realistic scenario for gene interactions in general. Smoothness and sparsity of network changes with time are also discussed. We would like to stress that the method is easily extendable to model nonlinear interactions. Moreover, the proposed methodology is applicable in any type of time varying network including various other biological processes where variables evolve in relation to each other.