# Lifted Causal Inference

arXiv: https://arxiv.org/abs/2606.28024 · HTML: https://mlsanity.com/paper/2606.28024/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 53 references that are in the map.
- First posted on arXiv 26 Jun 2026.

## Builds on (most cited first, 16 of 16)

- [Tractability through Exchangeability: A New Perspective on Efficient Probabilistic Inference](https://mlsanity.com/paper/1401.1247/) (2014)
- [Estimating the effect of joint interventions from observational data in sparse high-dimensional settings](https://mlsanity.com/paper/1407.2451/) (2014)
- [Lifted Variable Elimination: Decoupling the Operators from the Constraint Language](https://mlsanity.com/paper/1402.0565/) (2014)
- [Bayes-Ball: The Rational Pastime (for Determining Irrelevance and Requisite Information in Belief Networks and Influence Diagrams)](https://mlsanity.com/paper/1301.7412/) (2013)
- [An Algorithm for Deciding if a Set of Observed Independencies Has a Causal Explanation](https://mlsanity.com/paper/1303.5435/) (2013)
- [Causal Relational Learning](https://mlsanity.com/paper/2004.03644/) (2020)
- [A Sound and Complete Algorithm for Learning Causal Models from Relational Data](https://mlsanity.com/paper/1309.6843/) (2013)
- [Minimal enumeration of all possible total effects in a Markov equivalence class](https://mlsanity.com/paper/2010.08611/) (2020)
- [Towards Robust Relational Causal Discovery](https://mlsanity.com/paper/1912.02390/) (2019)
- [Taming Reasoning in Temporal Probabilistic Relational Models](https://mlsanity.com/paper/1911.07040/) (2019)
- [Lifted Causal Inference in Relational Domains](https://mlsanity.com/paper/2403.10184/) (2024)
- [Learning Relational Causal Models with Cycles through Relational Acyclification](https://mlsanity.com/paper/2208.12210/) (2022)
- [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)
- [Estimating Causal Effects in Partially Directed Parametric Causal Factor Graphs](https://mlsanity.com/paper/2411.07006/) (2024)
- [Practical Algorithms for Orientations of Partially Directed Graphical Models](https://mlsanity.com/paper/2302.14386/) (2023)

## Abstract (arXiv)

Lifted inference exploits indistinguishabilities in probabilistic graphical models by using a representative for indistinguishable objects, thereby speeding up query answering while maintaining exact answers. In this article, we show how lifting can be applied to efficiently compute causal effects in relational domains. More specifically, we introduce parametric causal factor graphs (PCFGs) to incorporate causal knowledge in lifted models and give a formal semantics of interventions therein. We further present the Lifted Causal Inference (LCI) algorithm to compute causal effects on a lifted level, thereby drastically speeding up causal inference compared to propositional inference, e.g., in causal Bayesian networks. In addition, we present partially directed parametric causal factor graphs (PD-PCFGs) as a generalisation of PCFGs to handle partial causal knowledge and extend LCI to perform lifted causal inference in a PD-PCFG, thereby extending the applicability of lifted causal inference to a broader range of models requiring less prior knowledge about causal relationships.