# Sample Constrained Treatment Effect Estimation

arXiv: https://arxiv.org/abs/2210.06594 · HTML: https://mlsanity.com/paper/2210.06594/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 56 references that are in the map.
- First posted on arXiv 12 Oct 2022.

## Builds on (most cited first, 21 of 21)

- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Causal Effect Inference with Deep Latent-Variable Models](https://mlsanity.com/paper/1705.08821/) (2017)
- [Sketching as a Tool for Numerical Linear Algebra](https://mlsanity.com/paper/1411.4357/) (2014)
- [Recursive Partitioning for Heterogeneous Causal Effects](https://mlsanity.com/paper/1504.01132/) (2015)
- [Learning Causal Graphs with Small Interventions](https://mlsanity.com/paper/1511.00041/) (2015)
- [Cost-Optimal Learning of Causal Graphs](https://mlsanity.com/paper/1703.02645/) (2017)
- [Graph cluster randomization: network exposure to multiple universes](https://mlsanity.com/paper/1305.6979/) (2013)
- [A Statistical Perspective on Algorithmic Leveraging](https://mlsanity.com/paper/1306.5362/) (2013)
- [Budgeted Experiment Design for Causal Structure Learning](https://mlsanity.com/paper/1709.03625/) (2017)
- [Budgeted and Non-budgeted Causal Bandits](https://mlsanity.com/paper/2012.07058/) (2020)
- [Active Regression via Linear-Sample Sparsification](https://mlsanity.com/paper/1711.10051/) (2017)
- [Discrepancy, Coresets, and Sketches in Machine Learning](https://mlsanity.com/paper/1906.04845/) (2019)
- [Causal-BALD: Deep Bayesian Active Learning of Outcomes to Infer Treatment-Effects from Observational Data](https://mlsanity.com/paper/2111.02275/) (2021)
- [Efficient Intervention Design for Causal Discovery with Latents](https://mlsanity.com/paper/2005.11736/) (2020)
- [Best Arm Identification in Generalized Linear Bandits](https://mlsanity.com/paper/1905.08224/) (2019)
- [Active Learning for Decision-Making from Imbalanced Observational Data](https://mlsanity.com/paper/1904.05268/) (2019)
- [High-dimensional regression adjustments in randomized experiments](https://mlsanity.com/paper/1607.06801/) (2016)
- [The Gram-Schmidt Walk: A Cure for the Banaszczyk Blues](https://mlsanity.com/paper/1708.01079/) (2017)
- [Intervention Efficient Algorithms for Approximate Learning of Causal Graphs](https://mlsanity.com/paper/2012.13976/) (2020)
- [Sublinear-Time Non-Adaptive Group Testing with O(k log n) Tests via Bit-Mixing Coding](https://mlsanity.com/paper/1904.10102/) (2019)
- [Efficient Balanced Treatment Assignments for Experimentation](https://mlsanity.com/paper/2010.11332/) (2020)

## Built on by (most cited first, 7 of 7)

- [Progressive Generalization Risk Reduction for Data-Efficient Causal Effect Estimation](https://mlsanity.com/paper/2411.11256/) (2024)
- [Enhancing Treatment Effect Estimation via Active Learning: A Counterfactual Covering Perspective](https://mlsanity.com/paper/2505.05242/) (2025)
- [Task-specific experimental design for treatment effect estimation](https://mlsanity.com/paper/2306.05484/) (2023)
- [Causal-EPIG: A Prediction-Oriented Active Learning Framework for CATE Estimation](https://mlsanity.com/paper/2509.21866/) (2025)
- [Benchmarking Estimators for Natural Experiments: A Novel Dataset and a Doubly Robust Algorithm](https://mlsanity.com/paper/2409.04500/) (2024)
- [Observationally Informed Adaptive Causal Experimental Design](https://mlsanity.com/paper/2603.03785/) (2026)
- [Limits of Approximating the Median Treatment Effect](https://mlsanity.com/paper/2403.10618/) (2024)

## Abstract (arXiv)

Treatment effect estimation is a fundamental problem in causal inference. We focus on designing efficient randomized controlled trials, to accurately estimate the effect of some treatment on a population of n individuals. In particular, we study sample-constrained treatment effect estimation, where we must select a subset of s ll n individuals from the population to experiment on. This subset must be further partitioned into treatment and control groups. Algorithms for partitioning the entire population into treatment and control groups, or for choosing a single representative subset, have been well-studied. The key challenge in our setting is jointly choosing a representative subset and a partition for that set. We focus on both individual and average treatment effect estimation, under a linear effects model. We give provably efficient experimental designs and corresponding estimators, by identifying connections to discrepancy minimization and leverage-score-based sampling used in randomized numerical linear algebra. Our theoretical results obtain a smooth transition to known guarantees when s equals the population size. We also empirically demonstrate the performance of our algorithms.