Uncertainty quantification and posterior sampling for network reconstruction
This addresses the limitation of point estimates in network reconstruction for researchers in fields like systems biology or social network analysis, offering a more robust statistical framework, though it is incremental in improving existing methods.
The paper tackles the problem of network reconstruction, which is ill-posed and often yields multiple plausible solutions, by developing an efficient MCMC algorithm to sample from posterior distributions, enabling full uncertainty quantification and improving reconstruction accuracy.
Network reconstruction is the task of inferring the unseen interactions between elements of a system, based only on their behavior or dynamics. This inverse problem is in general ill-posed, and admits many solutions for the same observation. Nevertheless, the vast majority of statistical methods proposed for this task -- formulated as the inference of a graphical generative model -- can only produce a ``point estimate,'' i.e. a single network considered the most likely. In general, this can give only a limited characterization of the reconstruction, since uncertainties and competing answers cannot be conveyed, even if their probabilities are comparable, while being structurally different. In this work we present an efficient MCMC algorithm for sampling from posterior distributions of reconstructed networks, which is able to reveal the full population of answers for a given reconstruction problem, weighted according to their plausibilities. Our algorithm is general, since it does not rely on specific properties of particular generative models, and is specially suited for the inference of large and sparse networks, since in this case an iteration can be performed in time $O(N\log^2 N)$ for a network of $N$ nodes, instead of $O(N^2)$, as would be the case for a more naive approach. We demonstrate the suitability of our method in providing uncertainties and consensus of solutions (which provably increases the reconstruction accuracy) in a variety of synthetic and empirical cases.