# Uncertainty quantification and posterior sampling for network reconstruction

arXiv: https://arxiv.org/abs/2503.07736 · HTML: https://mlsanity.com/paper/2503.07736/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 50 references that are in the map.
- First posted on arXiv 10 Mar 2025.

## Builds on (most cited first, 12 of 12)

- [Hierarchical Block Structures and High-resolution Model Selection in Large Networks](https://mlsanity.com/paper/1310.4377/) (2013)
- [Inverse statistical problems: from the inverse Ising problem to data science](https://mlsanity.com/paper/1702.01522/) (2017)
- [Nonparametric Bayesian inference of the microcanonical stochastic block model](https://mlsanity.com/paper/1610.02703/) (2016)
- [Network structure from rich but noisy data](https://mlsanity.com/paper/1703.07376/) (2017)
- [Network reconstruction and community detection from dynamics](https://mlsanity.com/paper/1903.10833/) (2019)
- [A convex pseudo-likelihood framework for high dimensional partial correlation estimation with convergence guarantees](https://mlsanity.com/paper/1307.5381/) (2013)
- [Reconstructing networks with unknown and heterogeneous errors](https://mlsanity.com/paper/1806.07956/) (2018)
- [Merge-split Markov chain Monte Carlo for community detection](https://mlsanity.com/paper/2003.07070/) (2020)
- [Network reconstruction from infection cascades](https://mlsanity.com/paper/1609.00432/) (2016)
- [Latent Poisson models for networks with heterogeneous density](https://mlsanity.com/paper/2002.07803/) (2020)
- [Network reconstruction via the minimum description length principle](https://mlsanity.com/paper/2405.01015/) (2024)
- [Scalable network reconstruction in subquadratic time](https://mlsanity.com/paper/2401.01404/) (2024)

## Built on by (most cited first, 1 of 1)

- [GraIP: A Benchmarking Framework For Neural Graph Inverse Problems](https://mlsanity.com/paper/2601.18917/) (2026)

## Abstract (arXiv)

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(Nlog2 N) for a network of N nodes, instead of O(N2), 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.