# ION-C: Integration of Overlapping Networks via Constraints

arXiv: https://arxiv.org/abs/2411.04243 · HTML: https://mlsanity.com/paper/2411.04243/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 33 references that are in the map.
- First posted on arXiv 6 Nov 2024.

## Builds on (most cited first, 8 of 8)

- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Multi-shot ASP solving with clingo](https://mlsanity.com/paper/1705.09811/) (2017)
- [Causal-learn: Causal Discovery in Python](https://mlsanity.com/paper/2307.16405/) (2023)
- [Vertical Federated Learning: Challenges, Methodologies and Experiments](https://mlsanity.com/paper/2202.04309/) (2022)
- [Causal Discovery in the Presence of Missing Data](https://mlsanity.com/paper/1807.04010/) (2018)
- [Secure and Efficient Federated Transfer Learning](https://mlsanity.com/paper/1910.13271/) (2019)
- [Discovering Cyclic Causal Models with Latent Variables: A General SAT-Based Procedure](https://mlsanity.com/paper/1309.6836/) (2013)
- [GRACE-C: Generalized Rate Agnostic Causal Estimation via Constraints](https://mlsanity.com/paper/2205.09235/) (2022)

## Abstract (arXiv)

In many causal learning problems, variables of interest are often not all measured over the same observations, but are instead distributed across multiple datasets with overlapping variables. Tillman et al. (2008) presented the first algorithm for enumerating the minimal equivalence class of ground-truth DAGs consistent with all input graphs by exploiting local independence relations, called ION. In this paper, this problem is formulated as a more computationally efficient answer set programming (ASP) problem, which we call ION-C, and solved with the ASP system clingo. The ION-C algorithm was run on random synthetic graphs with varying sizes, densities, and degrees of overlap between subgraphs, with overlap having the largest impact on runtime, number of solution graphs, and agreement within the output set. To validate ION-C on real-world data, we ran the algorithm on overlapping graphs learned from data from two successive iterations of the European Social Survey (ESS), using a procedure for conducting joint independence tests to prevent inconsistencies in the input.