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Uncertainty quantification and posterior sampling for network reconstruction
Title / Series / Name
Proceedings of the Royal Society A-mathematical Physical and Engineering Sciences
Publication Volume
481
Publication Issue
2325
Pages
Authors
Editors
Keywords
Network reconstruction
Posterior sampling
Uncertainty quantification
General Mathematics
General Engineering
General Physics and Astronomy
Posterior sampling
Uncertainty quantification
General Mathematics
General Engineering
General Physics and Astronomy
URI
https://hdl.handle.net/20.500.14018/28689
Abstract
Network reconstruction is the task of inferring the unseen interactions between elements of a system, based only on their behaviour 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 Markov-chain Monte–Carlo 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(Nlog2 N) for a network of N nodes, instead of O(N2), as would be the case for a more naïve 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.
Topic
Publisher
Place of Publication
Type
Journal article
Date
2025-11-05
Language
ISBN
Identifiers
10.1098/rspa.2025.0344