# Causal Imputation via Synthetic Interventions

arXiv: https://arxiv.org/abs/2011.03127 · HTML: https://mlsanity.com/paper/2011.03127/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Nov 2020.

## Built on by (most cited first, 13 of 13)

- [Causal Deep Learning](https://mlsanity.com/paper/2303.02186/) (2023)
- [Simple, Fast, and Flexible Framework for Matrix Completion with Infinite Width Neural Networks](https://mlsanity.com/paper/2108.00131/) (2021)
- [Intervention Generalization: A View from Factor Graph Models](https://mlsanity.com/paper/2306.04027/) (2023)
- [Adaptive Principal Component Regression with Applications to Panel Data](https://mlsanity.com/paper/2307.01357/) (2023)
- [Enforcing Conditional Independence for Fair Representation Learning and Causal Image Generation](https://mlsanity.com/paper/2404.13798/) (2024)
- [Synthetic Potential Outcomes and Causal Mixture Identifiability](https://mlsanity.com/paper/2405.19225/) (2024)
- [Entropic Causal Inference: Graph Identifiability](https://mlsanity.com/paper/2509.16463/) (2025)
- [Causal Imputation for Counterfactual SCMs: Bridging Graphs and Latent Factor Models](https://mlsanity.com/paper/2402.14777/) (2024)
- [Structured Learning of Compositional Sequential Interventions](https://mlsanity.com/paper/2406.05745/) (2024)
- [Covariate-Adjusted Deep Causal Learning for Heterogeneous Panel Data Models](https://mlsanity.com/paper/2505.20536/) (2025)
- [General Causal Imputation via Synthetic Interventions](https://mlsanity.com/paper/2410.20647/) (2024)
- [SystemMatch: optimizing preclinical drug models to human clinical outcomes via generative latent-space matching](https://mlsanity.com/paper/2205.07110/) (2022)
- [Extrapolation Guarantees for Perturbation Modeling Under the Additive Latent Shift Assumption](https://mlsanity.com/paper/2504.18522/) (2025)

## Abstract (arXiv)

Consider the problem of determining the effect of a compound on a specific cell type. To answer this question, researchers traditionally need to run an experiment applying the drug of interest to that cell type. This approach is not scalable: given a large number of different actions (compounds) and a large number of different contexts (cell types), it is infeasible to run an experiment for every action-context pair. In such cases, one would ideally like to predict the outcome for every pair while only having to perform experiments on a small subset of pairs. This task, which we label "causal imputation", is a generalization of the causal transportability problem. To address this challenge, we extend the recently introduced synthetic interventions (SI) estimator to handle more general data sparsity patterns. We prove that, under a latent factor model, our estimator provides valid estimates for the causal imputation task. We motivate this model by establishing a connection to the linear structural causal model literature. Finally, we consider the prominent CMAP dataset in predicting the effects of compounds on gene expression across cell types. We find that our estimator outperforms standard baselines, thus confirming its utility in biological applications.