# Causal Models for Growing Networks

arXiv: https://arxiv.org/abs/2504.01012 · HTML: https://mlsanity.com/paper/2504.01012/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 44 references that are in the map.
- First posted on arXiv 1 Apr 2025.

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

- [Bayesian Models of Graphs, Arrays and Other Exchangeable Random Structures](https://mlsanity.com/paper/1312.7857/) (2013)
- [A Probabilistic Calculus of Actions](https://mlsanity.com/paper/1302.6835/) (2013)
- [Causal models in string diagrams](https://mlsanity.com/paper/2304.07638/) (2023)
- [Compositionality as we see it, everywhere around us](https://mlsanity.com/paper/2110.05327/) (2021)
- [Towards fully covariant machine learning](https://mlsanity.com/paper/2301.13724/) (2023)
- [Causal Modeling With Infinitely Many Variables](https://mlsanity.com/paper/2112.09171/) (2021)
- [Intervention Generalization: A View from Factor Graph Models](https://mlsanity.com/paper/2306.04027/) (2023)
- [A Directed Preferential Attachment Model with Poisson Measurement](https://mlsanity.com/paper/2008.07005/) (2020)
- [Structure and dynamics of growing networks of Reddit threads](https://mlsanity.com/paper/2409.04085/) (2024)
- [Triangle Preferential Attachment Has Power-law Degrees and Eigenvalues; Eigenvalues Are More Stable to Network Sampling](https://mlsanity.com/paper/1904.12989/) (2019)
- [Insights and caveats from mining local and global temporal motifs in cryptocurrency transaction networks](https://mlsanity.com/paper/2402.09272/) (2024)
- [Quantifying Human Priors over Social and Navigation Networks](https://mlsanity.com/paper/2402.18651/) (2024)

## Abstract (arXiv)

Real-world networks grow over time; statistical models based on node exchangeability are not appropriate. Instead of constraining the structure of the textitdistribution of edges, we propose that the relevant symmetries refer to the textitcausal structure between them. We first enumerate the 96 causal directed acyclic graph (DAG) models over pairs of nodes (dyad variables) in a growing network with finite ancestral sets that are invariant to node deletion. We then partition them into 21 classes with ancestral sets that are closed under node marginalization. Several of these classes are remarkably amenable to distributed and asynchronous evaluation. As an example, we highlight a simple model that exhibits flexible power-law degree distributions and emergent phase transitions in sparsity, which we characterize analytically. With few parameters and much conditional independence, our proposed framework provides natural baseline models for causal inference in relational data.