# Inferring Dynamic Networks from Marginals with Iterative Proportional Fitting

arXiv: https://arxiv.org/abs/2402.18697 · HTML: https://mlsanity.com/paper/2402.18697/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 87 references that are in the map.
- First posted on arXiv 28 Feb 2024.

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

- [Estimation from Pairwise Comparisons: Sharp Minimax Bounds with Topology Dependence](https://mlsanity.com/paper/1505.01462/) (2015)
- [Network Inference via the Time-Varying Graphical Lasso](https://mlsanity.com/paper/1703.01958/) (2017)
- [A gradient descent perspective on Sinkhorn](https://mlsanity.com/paper/2002.03758/) (2020)
- [Network Inference and Influence Maximization from Samples](https://mlsanity.com/paper/2106.03403/) (2021)
- [Approximation Algorithms for Reducing the Spectral Radius to Control Epidemic Spread](https://mlsanity.com/paper/1501.06614/) (2015)
- [Learning to Infer Structures of Network Games](https://mlsanity.com/paper/2206.08119/) (2022)
- [Learning Rich Rankings](https://mlsanity.com/paper/2312.15081/) (2023)
- [On Sinkhorn's Algorithm and Choice Modeling](https://mlsanity.com/paper/2310.00260/) (2023)
- [Leveraging Administrative Data for Bias Audits: Assessing Disparate Coverage with Mobility Data for COVID-19 Policy](https://mlsanity.com/paper/2011.07194/) (2020)
- [ChoiceRank: Identifying Preferences from Node Traffic in Networks](https://mlsanity.com/paper/1610.06525/) (2016)
- [Optimal Intervention on Weighted Networks via Edge Centrality](https://mlsanity.com/paper/2303.09086/) (2023)
- [Strategic Choices of Migrants and Smugglers in the Central Mediterranean Sea](https://mlsanity.com/paper/2207.04480/) (2022)

## Built on by (most cited first, 3 of 3)

- [Transfer Learning for Latent Variable Network Models](https://mlsanity.com/paper/2406.03437/) (2024)
- [Learning production functions for supply chains with graph neural networks](https://mlsanity.com/paper/2407.18772/) (2024)
- [Learning Demographic-Conditioned Mobility Trajectories with Aggregate Supervision](https://mlsanity.com/paper/2603.03275/) (2026)

## Abstract (arXiv)

A common network inference problem, arising from real-world data constraints, is how to infer a dynamic network from its time-aggregated adjacency matrix and time-varying marginals (i.e., row and column sums). Prior approaches to this problem have repurposed the classic iterative proportional fitting (IPF) procedure, also known as Sinkhorn's algorithm, with promising empirical results. However, the statistical foundation for using IPF has not been well understood: under what settings does IPF provide principled estimation of a dynamic network from its marginals, and how well does it estimate the network? In this work, we establish such a setting, by identifying a generative network model whose maximum likelihood estimates are recovered by IPF. Our model both reveals implicit assumptions on the use of IPF in such settings and enables new analyses, such as structure-dependent error bounds on IPF's parameter estimates. When IPF fails to converge on sparse network data, we introduce a principled algorithm that guarantees IPF converges under minimal changes to the network structure. Finally, we conduct experiments with synthetic and real-world data, which demonstrate the practical value of our theoretical and algorithmic contributions.