Abstract
Inferring causal structures of real world complex networks from measured time series signals remains an open issue. The current approaches are inadequate to discern between direct versus indirect influences (i.e., the presence or absence of a directed arc connecting two nodes) in the presence of noise, sparse interactions, as well as nonlinear and transient dynamics of real world processes. We report a sparse regression (referred to as the -min) approach with theoretical bounds on the constraints on the allowable perturbation to recover the network structure that guarantees sparsity and robustness to noise. We also introduce averaging and perturbation procedures to further enhance prediction scores (i.e., reduce inference errors), and the numerical stability of -min approach. Extensive investigations have been conducted with multiple benchmark simulated genetic regulatory network and Michaelis-Menten dynamics, as well as real world data sets from DREAM5 challenge. These investigations suggest that our approach can significantly improve, oftentimes by 5 orders of magnitude over the methods reported previously for inferring the structure of dynamic networks, such as Bayesian network, network deconvolution, silencing and modular response analysis methods based on optimizing for sparsity, transients, noise and high dimensionality issues.
Highlights
Inferring causal structures of real world complex networks from measured time series signals remains an open issue
Extensive investigations have been conducted with multiple benchmark simulated genetic regulatory network and Michaelis-Menten dynamics, as well as real world data sets from DREAM5 challenge. These investigations suggest that our approach can significantly improve, oftentimes by 5 orders of magnitude over the methods reported previously for inferring the structure of dynamic networks, such as Bayesian network, network deconvolution, silencing and modular response analysis methods based on optimizing for sparsity, transients, noise and high dimensionality issues
The second case study is an application of our method to infer genetic regulatory networks (GRNs) from empirical data in the context of DREAM5 challenge46
Summary
Inferring causal structures of real world complex networks from measured time series signals remains an open issue. Extensive investigations have been conducted with multiple benchmark simulated genetic regulatory network and Michaelis-Menten dynamics, as well as real world data sets from DREAM5 challenge These investigations suggest that our approach can significantly improve, oftentimes by 5 orders of magnitude over the methods reported previously for inferring the structure of dynamic networks, such as Bayesian network, network deconvolution, silencing and modular response analysis methods based on optimizing for sparsity, transients, noise and high dimensionality issues. Our main contribution is in providing a theoretical bound on the constraints of the 1-min formulation and providing stable numerical procedures that overcome effects of nonlinear couplings in large interconnected processes, availability of only a small sample of short time series ensembles, and inaccuracies in estimating noise levels. It is shown that up to 5 orders of magnitude reduction in the inference error are possible from the present approach, leading to a more accurate inference of the network structure for complex real world networks
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