# Compositional Models for Estimating Causal Effects

arXiv: https://arxiv.org/abs/2406.17714 · HTML: https://mlsanity.com/paper/2406.17714/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 73 references that are in the map.
- First posted on arXiv 25 Jun 2024.

## Builds on (most cited first, 28 of 28)

- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Meta-learners for Estimating Heterogeneous Treatment Effects using Machine Learning](https://mlsanity.com/paper/1706.03461/) (2017)
- [Neural Module Networks](https://mlsanity.com/paper/1511.02799/) (2015)
- [Learning Representations for Counterfactual Inference](https://mlsanity.com/paper/1605.03661/) (2016)
- [Improved Semantic Representations From Tree-Structured Long Short-Term Memory Networks](https://mlsanity.com/paper/1503.00075/) (2015)
- [Compositionality decomposed: how do neural networks generalise?](https://mlsanity.com/paper/1908.08351/) (2019)
- [Recursive Partitioning for Heterogeneous Causal Effects](https://mlsanity.com/paper/1504.01132/) (2015)
- [Nonparametric Estimation of Heterogeneous Treatment Effects: From Theory to Learning Algorithms](https://mlsanity.com/paper/2101.10943/) (2021)
- [MCP: Learning Composable Hierarchical Control with Multiplicative Compositional Policies](https://mlsanity.com/paper/1905.09808/) (2019)
- [Modular Deep Learning](https://mlsanity.com/paper/2302.11529/) (2023)
- [Generalization Bounds and Representation Learning for Estimation of Potential Outcomes and Causal Effects](https://mlsanity.com/paper/2001.07426/) (2020)
- [Compositional Generalization from First Principles](https://mlsanity.com/paper/2307.05596/) (2023)
- [Causal Effect Inference for Structured Treatments](https://mlsanity.com/paper/2106.01939/) (2021)
- [Is a Modular Architecture Enough?](https://mlsanity.com/paper/2206.02713/) (2022)
- [Plan-Structured Deep Neural Network Models for Query Performance Prediction](https://mlsanity.com/paper/1902.00132/) (2019)
- [Discovering modular solutions that generalize compositionally](https://mlsanity.com/paper/2312.15001/) (2023)
- [Image-based Treatment Effect Heterogeneity](https://mlsanity.com/paper/2206.06417/) (2022)
- [GraphITE: Estimating Individual Effects of Graph-structured Treatments](https://mlsanity.com/paper/2009.14061/) (2020)
- [ExeDec: Execution Decomposition for Compositional Generalization in Neural Program Synthesis](https://mlsanity.com/paper/2307.13883/) (2023)
- [Causal Relational Learning](https://mlsanity.com/paper/2004.03644/) (2020)
- [How and Why to Use Experimental Data to Evaluate Methods for Observational Causal Inference](https://mlsanity.com/paper/2010.03051/) (2020)
- [A Sound and Complete Algorithm for Learning Causal Models from Relational Data](https://mlsanity.com/paper/1309.6843/) (2013)
- [On the Assumptions of Synthetic Control Methods](https://mlsanity.com/paper/2112.05671/) (2021)
- [Hierarchical Causal Models](https://mlsanity.com/paper/2401.05330/) (2024)
- [Object-Oriented Bayesian Networks](https://mlsanity.com/paper/1302.1554/) (2013)
- [Learning Relational Causal Models with Cycles through Relational Acyclification](https://mlsanity.com/paper/2208.12210/) (2022)
- [What makes Models Compositional? A Theoretical View: With Supplement](https://mlsanity.com/paper/2405.02350/) (2024)

## Abstract (arXiv)

Many real-world systems can be usefully represented as sets of interacting components. Examples include computational systems, such as query processors and compilers, natural systems, such as cells and ecosystems, and social systems, such as families and organizations. However, current approaches to estimating potential outcomes and causal effects typically treat such systems as single units, represent them with a fixed set of variables, and assume a homogeneous data-generating process. In this work, we study a compositional approach for estimating individual-level potential outcomes and causal effects in structured systems, where each unit is represented by an instance-specific composition of multiple heterogeneous components. The compositional approach decomposes unit-level causal queries into more fine-grained queries, explicitly modeling how unit-level interventions affect component-level outcomes to generate a unit's outcome. We demonstrate this approach using modular neural network architectures and show that it provides benefits for causal effect estimation from observational data, such as accurate causal effect estimation for structured units, increased sample efficiency, improved overlap between treatment and control groups, and compositional generalization to units with unseen combinations of components. Remarkably, our results show that compositional modeling can improve the accuracy of causal estimation even when component-level outcomes are unobserved. We also create and use a set of real-world evaluation environments for the empirical evaluation of compositional approaches for causal effect estimation and demonstrate the role of composition structure, varying amounts of component-level data access, and component heterogeneity in the performance of compositional models as compared to the non-compositional approaches.