Research Article: Expectation propagation for large scale Bayesian inference of non-linear molecular networks from perturbation data

Date Published: February 6, 2017

Publisher: Public Library of Science

Author(s): Zahra Narimani, Hamid Beigy, Ashar Ahmad, Ali Masoudi-Nejad, Holger Fröhlich, Frank Emmert-Streib.


Inferring the structure of molecular networks from time series protein or gene expression data provides valuable information about the complex biological processes of the cell. Causal network structure inference has been approached using different methods in the past. Most causal network inference techniques, such as Dynamic Bayesian Networks and ordinary differential equations, are limited by their computational complexity and thus make large scale inference infeasible. This is specifically true if a Bayesian framework is applied in order to deal with the unavoidable uncertainty about the correct model. We devise a novel Bayesian network reverse engineering approach using ordinary differential equations with the ability to include non-linearity. Besides modeling arbitrary, possibly combinatorial and time dependent perturbations with unknown targets, one of our main contributions is the use of Expectation Propagation, an algorithm for approximate Bayesian inference over large scale network structures in short computation time. We further explore the possibility of integrating prior knowledge into network inference. We evaluate the proposed model on DREAM4 and DREAM8 data and find it competitive against several state-of-the-art existing network inference methods.

Partial Text

Cellular components function through their interaction in form of biological networks, such as regulatory and signaling pathways [1]. With the advances of experimental methods and the emergence of high-throughput techniques, such as DNA microarray and next generation sequencing, the measurement of expression values of genes on whole genome scale is now possible. These advances have motivated attempts to learn molecular networks from experimental data. However, network inference from experimental data is computationally nontrivial, because the number of variables (typically genes, or proteins) usually exceeds the number of samples. Moreover, the number of possible network structures increases super-exponentially with the number of network nodes. Therefore the search space to look for the true network is very large even for small graph instances and thus prevents the use of exact methods.

We proposed a Bayesian approach for computationally efficient inference of large scale molecular networks from complex perturbation data. Our FBISC method is highly flexible and applicable even in situations where the exact targets of perturbations are unknown (such as stress experiments), which is frequently the case in biology. A further strength is that we consider perturbations themselves as time dependent, as e.g. reflected in the DREAM4 data. FBISC uses a biochemically inspired model to describe the non-linear dynamical behavior of molecular networks and integrates this description into a graphical modeling framework. This allows for the application of efficient approximate inference schemes, such as expectation propagation. Notably, the output of our method is a posterior distribution over edge weights, which accounts for the unavoidable uncertainty of any network inference.




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