# Tractable Bounding of Counterfactual Queries by Knowledge Compilation

arXiv: https://arxiv.org/abs/2310.03352 · HTML: https://mlsanity.com/paper/2310.03352/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 14 references that are in the map.
- First posted on arXiv 5 Oct 2023.

## Builds on (most cited first, 9 of 9)

- [Partial Counterfactual Identification from Observational and Experimental Data](https://mlsanity.com/paper/2110.05690/) (2021)
- [An Automated Approach to Causal Inference in Discrete Settings](https://mlsanity.com/paper/2109.13471/) (2021)
- [Structural Causal Models Are (Solvable by) Credal Networks](https://mlsanity.com/paper/2008.00463/) (2020)
- [Causal Inference Using Tractable Circuits](https://mlsanity.com/paper/2202.02891/) (2022)
- [Causal Expectation-Maximisation](https://mlsanity.com/paper/2011.02912/) (2020)
- [Tractable Boolean and Arithmetic Circuits](https://mlsanity.com/paper/2202.02942/) (2022)
- [Partition Function Estimation: A Quantitative Study](https://mlsanity.com/paper/2105.11132/) (2021)
- [On the Complexity of Counterfactual Reasoning](https://mlsanity.com/paper/2211.13447/) (2022)
- [Bounding Counterfactuals under Selection Bias](https://mlsanity.com/paper/2208.01417/) (2022)

## Built on by (most cited first, 2 of 2)

- [Identifying Causal Effects Under Functional Dependencies](https://mlsanity.com/paper/2403.04919/) (2024)
- [Constrained Identifiability of Causal Effects](https://mlsanity.com/paper/2412.02869/) (2024)

## Abstract (arXiv)

We discuss the problem of bounding partially identifiable queries, such as counterfactuals, in Pearlian structural causal models. A recently proposed iterated EM scheme yields an inner approximation of those bounds by sampling the initialisation parameters. Such a method requires multiple (Bayesian network) queries over models sharing the same structural equations and topology, but different exogenous probabilities. This setup makes a compilation of the underlying model to an arithmetic circuit advantageous, thus inducing a sizeable inferential speed-up. We show how a single symbolic knowledge compilation allows us to obtain the circuit structure with symbolic parameters to be replaced by their actual values when computing the different queries. We also discuss parallelisation techniques to further speed up the bound computation. Experiments against standard Bayesian network inference show clear computational advantages with up to an order of magnitude of speed-up.