# Causal Unit Selection using Tractable Arithmetic Circuits

arXiv: https://arxiv.org/abs/2404.06681 · HTML: https://mlsanity.com/paper/2404.06681/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 33 references that are in the map.
- First posted on arXiv 10 Apr 2024.

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

- [A Differential Approach to Inference in Bayesian Networks](https://mlsanity.com/paper/1301.3847/) (2013)
- [On Relaxing Determinism in Arithmetic Circuits](https://mlsanity.com/paper/1708.06846/) (2017)
- [Counterfactuals and Policy Analysis in Structural Models](https://mlsanity.com/paper/1302.4929/) (2013)
- [Unit Selection with Nonbinary Treatment and Effect](https://mlsanity.com/paper/2208.09569/) (2022)
- [Solving Marginal MAP Exactly by Probabilistic Circuit Transformations](https://mlsanity.com/paper/2111.04833/) (2021)
- [Tractable Boolean and Arithmetic Circuits](https://mlsanity.com/paper/2202.02942/) (2022)
- [On the Complexity of Counterfactual Reasoning](https://mlsanity.com/paper/2211.13447/) (2022)
- [Unit Selection: Learning Benefit Function from Finite Population Data](https://mlsanity.com/paper/2210.08203/) (2022)
- [Unit Selection: Case Study and Comparison with A/B Test Heuristic](https://mlsanity.com/paper/2210.05030/) (2022)
- [An Algorithm and Complexity Results for Causal Unit Selection](https://mlsanity.com/paper/2302.14412/) (2023)

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

- [A Compositional Atlas for Algebraic Circuits](https://mlsanity.com/paper/2412.05481/) (2024)
- [Algorithmic causal structure emerging through compression](https://mlsanity.com/paper/2502.04210/) (2025)
- [Constrained Identifiability of Causal Effects](https://mlsanity.com/paper/2412.02869/) (2024)

## Abstract (arXiv)

The unit selection problem aims to find objects, called units, that optimize a causal objective function which describes the objects' behavior in a causal context (e.g., selecting customers who are about to churn but would most likely change their mind if encouraged). While early studies focused mainly on bounding a specific class of counterfactual objective functions using data, more recent work allows one to find optimal units exactly by reducing the causal objective to a classical objective on a meta-model, and then applying a variant of the classical Variable Elimination (VE) algorithm to the meta-model -- assuming a fully specified causal model is available. In practice, however, finding optimal units using this approach can be very expensive because the used VE algorithm must be exponential in the constrained treewidth of the meta-model, which is larger and denser than the original model. We address this computational challenge by introducing a new approach for unit selection that is not necessarily limited by the constrained treewidth. This is done through compiling the meta-model into a special class of tractable arithmetic circuits that allows the computation of optimal units in time linear in the circuit size. We finally present empirical results on random causal models that show order-of-magnitude speedups based on the proposed method for solving unit selection.