Dynamic Network Reconstruction from Heterogeneous Datasets.

Performing multiple experiments is common when learning internal mechanisms of complex systems. These experiments can include perturbations to parameters or external disturbances. A challenging problem is to efficiently incorporate all collected data simultaneously to infer the underlying dynamic network. This paper addresses the reconstruction of dynamic networks from heterogeneous datasets under the assumption that underlying networks share the same Boolean structure across all experiments. ARMAX models are used as an example to parametrize linear network models, known as "dynamical structure functions" (DSFs), which describe causal interactions between measured variables. Multiple datasets are integrated in one regression problem with additional demands of group sparsity to assure network sparsity and structure consistency. To perform group sparse estimation, we introduce and extend the iterative reweighted l1 method (with ADMM implementation), sparse Bayesian learning and sampling-based methods. Numerical examples illustrate the performance in random tests, which benchmark the proposed methods for stable ARX networks and DSF models. In summary, this paper presents an efficient network reconstruction method that takes advantage of all available data from multiple experiments, rather than processing datasets separately.