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Scalable network reconstruction in subquadratic time

Title / Series / Name
Proceedings of the Royal Society A-mathematical Physical and Engineering Sciences
Publication Volume
481
Publication Issue
2324
Pages
Authors
Peixoto, Tiago P.
Editors
Keywords
Complex networks
Network reconstruction
Statistical inference
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Peixoto-Tiago2_2025.pdf
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URI
https://hdl.handle.net/20.500.14018/28676
Abstract
Network reconstruction consists in determining the unobserved pairwise couplings between nodes given only observational data on the resulting behaviour that is conditioned on those couplings—typically a time-series or independent samples from a graphical model. A major obstacle to the scalability of algorithms proposed for this problem is a seemingly unavoidable quadratic complexity of ⁡(2), corresponding to the requirement of each possible pairwise coupling being contemplated at least once, despite the fact that most networks of interest are sparse, with a number of non-zero couplings that are only ⁡(). Here, we present a general algorithm applicable to a broad range of reconstruction problems that significantly outperforms this quadratic baseline. Our algorithm relies on a stochastic second-neighbour search that produces the best edge candidates with high probability, thus bypassing an exhaustive quadratic search. If we rely on the conjecture that the second-neighbour search finishes in log-linear time, we demonstrate theoretically that our algorithm finishes in subquadratic time, with a data-dependent complexity loosely upper bounded by ⁡(3/2⁢log⁡), but with a more typical log-linear complexity of ⁡(⁢log2⁡). In practice, we show that our algorithm achieves a performance that is many orders of magnitude faster than the quadratic baseline—in a manner consistent with our theoretical analysis—allows for easy parallelization, and thus enables the reconstruction of networks with hundreds of thousands and even millions of nodes and edges.
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Publisher
Place of Publication
Type
Journal article
Date
2025-10
Language
ISBN
Identifiers
10.1098/rspa.2025.0345
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Unit
Collections
Network and Data Science
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