# Learning Relational Causal Models with Cycles through Relational Acyclification

arXiv: https://arxiv.org/abs/2208.12210 · HTML: https://mlsanity.com/paper/2208.12210/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 34 references that are in the map.
- First posted on arXiv 25 Aug 2022.

## Builds on (most cited first, 13 of 13)

- [Foundations of Structural Causal Models with Cycles and Latent Variables](https://mlsanity.com/paper/1611.06221/) (2016)
- [backShift: Learning causal cyclic graphs from unknown shift interventions](https://mlsanity.com/paper/1506.02494/) (2015)
- [A Discovery Algorithm for Directed Cyclic Graphs](https://mlsanity.com/paper/1302.3599/) (2013)
- [Markov Properties for Graphical Models with Cycles and Latent Variables](https://mlsanity.com/paper/1710.08775/) (2017)
- [Constraint-Based Causal Discovery using Partial Ancestral Graphs in the presence of Cycles](https://mlsanity.com/paper/2005.00610/) (2020)
- [Directed Cyclic Graphical Representations of Feedback Models](https://mlsanity.com/paper/1302.4982/) (2013)
- [A Constraint-Based Algorithm For Causal Discovery with Cycles, Latent Variables and Selection Bias](https://mlsanity.com/paper/1805.02087/) (2018)
- [A Sound and Complete Algorithm for Learning Causal Models from Relational Data](https://mlsanity.com/paper/1309.6843/) (2013)
- [Causal inference, social networks, and chain graphs](https://mlsanity.com/paper/1812.04990/) (2018)
- [Towards Robust Relational Causal Discovery](https://mlsanity.com/paper/1912.02390/) (2019)
- [Lifted Representation of Relational Causal Models Revisited: Implications for Reasoning and Structure Learning](https://mlsanity.com/paper/1508.02103/) (2015)
- [Relational Causal Models with Cycles:Representation and Reasoning](https://mlsanity.com/paper/2202.10706/) (2022)
- [Reasoning about Independence in Probabilistic Models of Relational Data](https://mlsanity.com/paper/1302.4381/) (2013)

## Built on by (most cited first, 6 of 6)

- [Lifted Causal Inference in Relational Domains](https://mlsanity.com/paper/2403.10184/) (2024)
- [Relational Causal Discovery with Latent Confounders](https://mlsanity.com/paper/2507.01700/) (2025)
- [ORCA: ORchestrating Causal Agent](https://mlsanity.com/paper/2508.21304/) (2025)
- [Compositional Models for Estimating Causal Effects](https://mlsanity.com/paper/2406.17714/) (2024)
- [Position: Beyond Sensitive Attributes, ML Fairness Should Quantify Structural Injustice via Social Determinants](https://mlsanity.com/paper/2508.08337/) (2025)
- [Lifted Causal Inference](https://mlsanity.com/paper/2606.28024/) (2026)

## Abstract (arXiv)

In real-world phenomena which involve mutual influence or causal effects between interconnected units, equilibrium states are typically represented with cycles in graphical models. An expressive class of graphical models, relational causal models, can represent and reason about complex dynamic systems exhibiting such cycles or feedback loops. Existing cyclic causal discovery algorithms for learning causal models from observational data assume that the data instances are independent and identically distributed which makes them unsuitable for relational causal models. At the same time, causal discovery algorithms for relational causal models assume acyclicity. In this work, we examine the necessary and sufficient conditions under which a constraint-based relational causal discovery algorithm is sound and complete for cyclic relational causal models. We introduce relational acyclification, an operation specifically designed for relational models that enables reasoning about the identifiability of cyclic relational causal models. We show that under the assumptions of relational acyclification and σ-faithfulness, the relational causal discovery algorithm RCD (Maier et al. 2013) is sound and complete for cyclic models. We present experimental results to support our claim.