# Synthetic Interventions

arXiv: https://arxiv.org/abs/2006.07691 · HTML: https://mlsanity.com/paper/2006.07691/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jun 2020.

## Built on by (most cited first, 26 of 26)

- [Causal Matrix Completion](https://mlsanity.com/paper/2109.15154/) (2021)
- [Counterfactual (Non-)identifiability of Learned Structural Causal Models](https://mlsanity.com/paper/2301.09031/) (2023)
- [Synthetic Combinations: A Causal Inference Framework for Combinatorial Interventions](https://mlsanity.com/paper/2303.14226/) (2023)
- [PerSim: Data-Efficient Offline Reinforcement Learning with Heterogeneous Agents via Personalized Simulators](https://mlsanity.com/paper/2102.06961/) (2021)
- [CausalSim: A Causal Framework for Unbiased Trace-Driven Simulation](https://mlsanity.com/paper/2201.01811/) (2022)
- [On counterfactual inference with unobserved confounding](https://mlsanity.com/paper/2211.08209/) (2022)
- [Doubly robust nearest neighbors in factor models](https://mlsanity.com/paper/2211.14297/) (2022)
- [Adaptive Principal Component Regression with Applications to Panel Data](https://mlsanity.com/paper/2307.01357/) (2023)
- [Strategyproof Decision-Making in Panel Data Settings and Beyond](https://mlsanity.com/paper/2211.14236/) (2022)
- [Synthetic Potential Outcomes and Causal Mixture Identifiability](https://mlsanity.com/paper/2405.19225/) (2024)
- [SCouT: Synthetic Counterfactuals via Spatiotemporal Transformers for Actionable Healthcare](https://mlsanity.com/paper/2207.04208/) (2022)
- [Heterogeneous Synthetic Learner for Panel Data](https://mlsanity.com/paper/2212.14580/) (2022)
- [Causal Customer Churn Analysis with Low-rank Tensor Block Hazard Model](https://mlsanity.com/paper/2405.11377/) (2024)
- [Structured Learning of Compositional Sequential Interventions](https://mlsanity.com/paper/2406.05745/) (2024)
- [Learning Counterfactual Distributions via Kernel Nearest Neighbors](https://mlsanity.com/paper/2410.13381/) (2024)
- [Covariate-Adjusted Deep Causal Learning for Heterogeneous Panel Data Models](https://mlsanity.com/paper/2505.20536/) (2025)
- [Causal Inference with Categorical Unobserved Confounder via Mixture Learning](https://mlsanity.com/paper/2605.19006/) (2026)
- [Two-Sided Nearest Neighbors: An adaptive and minimax optimal procedure for matrix completion](https://mlsanity.com/paper/2411.12965/) (2024)
- [Adaptively-weighted Nearest Neighbors for Matrix Completion](https://mlsanity.com/paper/2505.09612/) (2025)
- [Bounded (O(1)) Regret Recommendation Learning via Synthetic Controls Oracle](https://mlsanity.com/paper/2301.12571/) (2023)
- [Incentive-Aware Synthetic Control: Accurate Counterfactual Estimation via Incentivized Exploration](https://mlsanity.com/paper/2312.16307/) (2023)
- [Extrapolation Guarantees for Perturbation Modeling Under the Additive Latent Shift Assumption](https://mlsanity.com/paper/2504.18522/) (2025)
- [A Vision Toward Energy-Efficient Domain-Specific Artificial Intelligence Models and Agents](https://mlsanity.com/paper/2510.22052/) (2025)
- [Efficiently Learning Synthetic Control Models for High-dimensional Disaggregated Data](https://mlsanity.com/paper/2510.22828/) (2025)
- [Counterfactual Forecasting for Panel Data](https://mlsanity.com/paper/2511.06189/) (2025)
- [Causal Matrix Completion under Multiple Treatments via Mixed Synthetic Nearest Neighbors](https://mlsanity.com/paper/2603.11942/) (2026)

## Abstract (arXiv)

The synthetic controls (SC) methodology is a prominent tool for policy evaluation in panel data applications. Researchers commonly justify the SC framework with a low-rank matrix factor model that assumes the potential outcomes are described by low-dimensional unit and time specific latent factors. In the recent work of [Abadie '20], one of the pioneering authors of the SC method posed the question of how the SC framework can be extended to multiple treatments. This article offers one resolution to this open question that we call synthetic interventions (SI). Fundamental to the SI framework is a low-rank tensor factor model, which extends the matrix factor model by including a latent factorization over treatments. Under this model, we propose a generalization of the standard SC-based estimators. We prove the consistency for one instantiation of our approach and provide conditions under which it is asymptotically normal. Moreover, we conduct a representative simulation to study its prediction performance and revisit the canonical SC case study of [Abadie-Diamond-Hainmueller '10] on the impact of anti-tobacco legislations by exploring related questions not previously investigated.