# Causal Inference Using Tractable Circuits

arXiv: https://arxiv.org/abs/2202.02891 · HTML: https://mlsanity.com/paper/2202.02891/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 38 references that are in the map.
- First posted on arXiv 7 Feb 2022.

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

- [A Differential Approach to Inference in Bayesian Networks](https://mlsanity.com/paper/1301.3847/) (2013)
- [Context-Specific Independence in Bayesian Networks](https://mlsanity.com/paper/1302.3562/) (2013)
- [Probabilistic Evaluation of Sequential Plans from Causal Models with Hidden Variables](https://mlsanity.com/paper/1302.4977/) (2013)
- [Identifying Causal Effects via Context-specific Independence Relations](https://mlsanity.com/paper/2009.09768/) (2020)
- [On Relaxing Determinism in Arithmetic Circuits](https://mlsanity.com/paper/1708.06846/) (2017)
- [Bucket Elimination: A Unifying Framework for Several Probabilistic Inference](https://mlsanity.com/paper/1302.3572/) (2013)
- [An Advance on Variable Elimination with Applications to Tensor-Based Computation](https://mlsanity.com/paper/2002.09320/) (2020)
- [Partition Function Estimation: A Quantitative Study](https://mlsanity.com/paper/2105.11132/) (2021)
- [Provable Guarantees on the Robustness of Decision Rules to Causal Interventions](https://mlsanity.com/paper/2105.09108/) (2021)
- [Binary Join Trees](https://mlsanity.com/paper/1302.3604/) (2013)

## Built on by (most cited first, 12 of 12)

- [Compositional Probabilistic and Causal Inference using Tractable Circuit Models](https://mlsanity.com/paper/2304.08278/) (2023)
- [Approximating Counterfactual Bounds while Fusing Observational, Biased and Randomised Data Sources](https://mlsanity.com/paper/2307.16577/) (2023)
- [Bounding Counterfactuals under Selection Bias](https://mlsanity.com/paper/2208.01417/) (2022)
- [Estimating Causal Effects from Learned Causal Networks](https://mlsanity.com/paper/2408.14101/) (2024)
- [Algorithmic causal structure emerging through compression](https://mlsanity.com/paper/2502.04210/) (2025)
- [Tractable Bounding of Counterfactual Queries by Knowledge Compilation](https://mlsanity.com/paper/2310.03352/) (2023)
- [An Algorithm and Complexity Results for Causal Unit Selection](https://mlsanity.com/paper/2302.14412/) (2023)
- [Learning to Bound Counterfactual Inference from Observational, Biased and Randomised Data](https://mlsanity.com/paper/2212.02932/) (2022)
- [Combining Local Symmetry Exploitation and Reinforcement Learning for Optimised Probabilistic Inference -- A Work In Progress](https://mlsanity.com/paper/2503.08786/) (2025)
- [Causal identification with Y0](https://mlsanity.com/paper/2508.03167/) (2025)
- [Causal Neural Probabilistic Circuits](https://mlsanity.com/paper/2603.01372/) (2026)
- [On Probabilistic Inference Through Parametric Tensor Decomposition in Base Tensor Networks](https://mlsanity.com/paper/2609.23774/) (2026)

## Abstract (arXiv)

The aim of this paper is to discuss a recent result which shows that probabilistic inference in the presence of (unknown) causal mechanisms can be tractable for models that have traditionally been viewed as intractable. This result was reported recently to facilitate model-based supervised learning but it can be interpreted in a causality context as follows. One can compile a non-parametric causal graph into an arithmetic circuit that supports inference in time linear in the circuit size. The circuit is also non-parametric so it can be used to estimate parameters from data and to further reason (in linear time) about the causal graph parametrized by these estimates. Moreover, the circuit size can sometimes be bounded even when the treewidth of the causal graph is not, leading to tractable inference on models that have been deemed intractable previously. This has been enabled by a new technique that can exploit causal mechanisms computationally but without needing to know their identities (the classical setup in causal inference). Our goal is to provide a causality-oriented exposure to these new results and to speculate on how they may potentially contribute to more scalable and versatile causal inference.