# Estimating Causal Effects in Partially Directed Parametric Causal Factor Graphs

arXiv: https://arxiv.org/abs/2411.07006 · HTML: https://mlsanity.com/paper/2411.07006/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 31 references that are in the map.
- First posted on arXiv 11 Nov 2024.

## Builds on (most cited first, 10 of 10)

- [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)
- [Minimal enumeration of all possible total effects in a Markov equivalence class](https://mlsanity.com/paper/2010.08611/) (2020)
- [Colour Passing Revisited: Lifted Model Construction with Commutative Factors](https://mlsanity.com/paper/2309.11236/) (2023)
- [Efficient Detection of Exchangeable Factors in Factor Graphs](https://mlsanity.com/paper/2403.10167/) (2024)
- [Lifted Causal Inference in Relational Domains](https://mlsanity.com/paper/2403.10184/) (2024)
- [Efficient Detection of Commutative Factors in Factor Graphs](https://mlsanity.com/paper/2407.16280/) (2024)
- [Lifting Factor Graphs with Some Unknown Factors](https://mlsanity.com/paper/2406.01275/) (2024)

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

- [Approximate Lifted Model Construction](https://mlsanity.com/paper/2504.20784/) (2025)
- [Lifted Model Construction without Normalisation: A Vectorised Approach to Exploit Symmetries in Factor Graphs](https://mlsanity.com/paper/2411.11730/) (2024)
- [Lifted Causal Inference](https://mlsanity.com/paper/2606.28024/) (2026)

## Abstract (arXiv)

Lifting uses a representative of indistinguishable individuals to exploit symmetries in probabilistic relational models, denoted as parametric factor graphs, to speed up inference while maintaining exact answers. In this paper, we show how lifting can be applied to causal inference in partially directed graphs, i.e., graphs that contain both directed and undirected edges to represent causal relationships between random variables. We present partially directed parametric causal factor graphs (PPCFGs) as a generalisation of previously introduced parametric causal factor graphs, which require a fully directed graph. We further show how causal inference can be performed on a lifted level in PPCFGs, thereby extending the applicability of lifted causal inference to a broader range of models requiring less prior knowledge about causal relationships.