Stability Indicators in Network Reconstruction

The number of algorithms available to reconstruct a biological network from a dataset of high-throughput measurements is nowadays overwhelming, but evaluating their performance when the gold standard is unknown is a difficult task. Here we propose to use a few reconstruction stability tools as a quantitative solution to this problem. We introduce four indicators to quantitatively assess the stability of a reconstructed network in terms of variability with respect to data subsampling. In particular, we give a measure of the mutual distances among the set of networks generated by a collection of data subsets (and from the network generated on the whole dataset) and we rank nodes and edges according to their decreasing variability within the same set of networks. As a key ingredient, we employ a global/local network distance combined with a bootstrap procedure. We demonstrate the use of the indicators in a controlled situation on a toy dataset, and we show their application on a miRNA microarray dataset with paired tumoral and non-tumoral tissues extracted from a cohort of 241 hepatocellular carcinoma patients

Network Reconstruction from Intrinsic Noise

This paper considers the problem of inferring an unknown network of dynamical systems driven by unknown, intrinsic, noise inputs. Equivalently we seek to identify direct causal dependencies among manifest variables only from observations of these variables. For linear, time-invariant systems of minimal order, we characterise under what conditions this problem is well posed. We first show that if the transfer matrix from the inputs to manifest states is minimum phase, this problem has a unique solution irrespective of the network topology. This is equivalent to there being only one valid spectral factor (up to a choice of signs of the inputs) of the output spectral density. If the assumption of phase-minimality is relaxed, we show that the problem is characterised by a single Algebraic Riccati Equation (ARE), of dimension determined by the number of latent states. The number of solutions to this ARE is an upper bound on the number of solutions for the network. We give necessary and sufficient conditions for any two dynamical networks to have equal output spectral density, which can be used to construct all equivalent networks. Extensive simulations quantify the number of solutions for a range of problem sizes. For a slightly simpler case, we also provide an algorithm to construct all equivalent networks from the output spectral density.Comment: 11 pages, submitted to IEEE Transactions on Automatic Contro

Network Reconstruction with Realistic Models

We extend a recently proposed gradient-matching method for inferring interactions in complex systems described by differential equations in various respects: improved gradient inference, evaluation of the influence of the prior on kinetic parameters, comparative evaluation of two model selection paradigms: marginal likelihood versus DIC (divergence information criterion), comparative evaluation of different numerical procedures for computing the marginal likelihood, extension of the methodology from protein phosphorylation to transcriptional regulation, based on a realistic simulation of the underlying molecular processes with Markov jump processes

Robust Network Reconstruction in Polynomial Time

This paper presents an efficient algorithm for robust network reconstruction of Linear Time-Invariant (LTI) systems in the presence of noise, estimation errors and unmodelled nonlinearities. The method here builds on previous work on robust reconstruction to provide a practical implementation with polynomial computational complexity. Following the same experimental protocol, the algorithm obtains a set of structurally-related candidate solutions spanning every level of sparsity. We prove the existence of a magnitude bound on the noise, which if satisfied, guarantees that one of these structures is the correct solution. A problem-specific model-selection procedure then selects a single solution from this set and provides a measure of confidence in that solution. Extensive simulations quantify the expected performance for different levels of noise and show that significantly more noise can be tolerated in comparison to the original method.Comment: 8 pages, to appear in 51st IEEE Conference on Decision and Contro

Multivariate Spatiotemporal Hawkes Processes and Network Reconstruction

There is often latent network structure in spatial and temporal data and the tools of network analysis can yield fascinating insights into such data. In this paper, we develop a nonparametric method for network reconstruction from spatiotemporal data sets using multivariate Hawkes processes. In contrast to prior work on network reconstruction with point-process models, which has often focused on exclusively temporal information, our approach uses both temporal and spatial information and does not assume a specific parametric form of network dynamics. This leads to an effective way of recovering an underlying network. We illustrate our approach using both synthetic networks and networks constructed from real-world data sets (a location-based social media network, a narrative of crime events, and violent gang crimes). Our results demonstrate that, in comparison to using only temporal data, our spatiotemporal approach yields improved network reconstruction, providing a basis for meaningful subsequent analysis --- such as community structure and motif analysis --- of the reconstructed networks