# Enhancing Treatment Effect Estimation via Active Learning: A Counterfactual Covering Perspective

arXiv: https://arxiv.org/abs/2505.05242 · HTML: https://mlsanity.com/paper/2505.05242/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 58 references that are in the map.
- First posted on arXiv 8 May 2025.

## Builds on (most cited first, 30 of 30)

- [Deep Bayesian Active Learning with Image Data](https://mlsanity.com/paper/1703.02910/) (2017)
- [Deep Batch Active Learning by Diverse, Uncertain Gradient Lower Bounds](https://mlsanity.com/paper/1906.03671/) (2019)
- [A Survey of Deep Active Learning](https://mlsanity.com/paper/2009.00236/) (2020)
- [Deep Kernel Learning](https://mlsanity.com/paper/1511.02222/) (2015)
- [Causal Effect Inference with Deep Latent-Variable Models](https://mlsanity.com/paper/1705.08821/) (2017)
- [Adapting Neural Networks for the Estimation of Treatment Effects](https://mlsanity.com/paper/1906.02120/) (2019)
- [Bayesian Inference of Individualized Treatment Effects using Multi-task Gaussian Processes](https://mlsanity.com/paper/1704.02801/) (2017)
- [A Comparative Survey of Deep Active Learning](https://mlsanity.com/paper/2203.13450/) (2022)
- [Gone Fishing: Neural Active Learning with Fisher Embeddings](https://mlsanity.com/paper/2106.09675/) (2021)
- [On Feature Collapse and Deep Kernel Learning for Single Forward Pass Uncertainty](https://mlsanity.com/paper/2102.11409/) (2021)
- [Bayesian Batch Active Learning as Sparse Subset Approximation](https://mlsanity.com/paper/1908.02144/) (2019)
- [Active Learning Through a Covering Lens](https://mlsanity.com/paper/2205.11320/) (2022)
- [Identifying Causal-Effect Inference Failure with Uncertainty-Aware Models](https://mlsanity.com/paper/2007.00163/) (2020)
- [Quantifying Ignorance in Individual-Level Causal-Effect Estimates under Hidden Confounding](https://mlsanity.com/paper/2103.04850/) (2021)
- [A Framework and Benchmark for Deep Batch Active Learning for Regression](https://mlsanity.com/paper/2203.09410/) (2022)
- [DeepMatch: Balancing Deep Covariate Representations for Causal Inference Using Adversarial Training](https://mlsanity.com/paper/1802.05664/) (2018)
- [Causal Inference under Networked Interference and Intervention Policy Enhancement](https://mlsanity.com/paper/2002.08506/) (2020)
- [Stochastic Batch Acquisition: A Simple Baseline for Deep Active Learning](https://mlsanity.com/paper/2106.12059/) (2021)
- [Benchmarking Framework for Performance-Evaluation of Causal Inference Analysis](https://mlsanity.com/paper/1802.05046/) (2018)
- [Pool-Based Sequential Active Learning for Regression](https://mlsanity.com/paper/1805.04735/) (2018)
- [Optimal Transport for Treatment Effect Estimation](https://mlsanity.com/paper/2310.18286/) (2023)
- [Learning Causal Effects on Hypergraphs](https://mlsanity.com/paper/2207.04049/) (2022)
- [Causal-BALD: Deep Bayesian Active Learning of Outcomes to Infer Treatment-Effects from Observational Data](https://mlsanity.com/paper/2111.02275/) (2021)
- [Doubly Robust Causal Effect Estimation under Networked Interference via Targeted Learning](https://mlsanity.com/paper/2405.03342/) (2024)
- [Linked Causal Variational Autoencoder for Inferring Paired Spillover Effects](https://mlsanity.com/paper/1808.03333/) (2018)
- [Active Learning for Decision-Making from Imbalanced Observational Data](https://mlsanity.com/paper/1904.05268/) (2019)
- [Sample Constrained Treatment Effect Estimation](https://mlsanity.com/paper/2210.06594/) (2022)
- [Estimating Treatment Effects Under Heterogeneous Interference](https://mlsanity.com/paper/2309.13884/) (2023)
- [Progressive Generalization Risk Reduction for Data-Efficient Causal Effect Estimation](https://mlsanity.com/paper/2411.11256/) (2024)
- [Task-specific experimental design for treatment effect estimation](https://mlsanity.com/paper/2306.05484/) (2023)

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

- [Causal-EPIG: A Prediction-Oriented Active Learning Framework for CATE Estimation](https://mlsanity.com/paper/2509.21866/) (2025)
- [Observationally Informed Adaptive Causal Experimental Design](https://mlsanity.com/paper/2603.03785/) (2026)
- [Treatment Effect Estimation with Differentiated Networked Effect on Graph Data](https://mlsanity.com/paper/2605.24358/) (2026)

## Abstract (arXiv)

Although numerous complex algorithms for treatment effect estimation have been developed in recent years, their effectiveness remains limited when handling insufficiently labeled training sets due to the high cost of labeling the effect after treatment, e.g., expensive tumor imaging or biopsy procedures needed to evaluate treatment effects. Therefore, it becomes essential to actively incorporate more high-quality labeled data, all while adhering to a constrained labeling budget. To enable data-efficient treatment effect estimation, we formalize the problem through rigorous theoretical analysis within the active learning context, where the derived key measures -- textitfactual and textitcounterfactual covering radius determine the risk upper bound. To reduce the bound, we propose a greedy radius reduction algorithm, which excels under an idealized, balanced data distribution. To generalize to more realistic data distributions, we further propose FCCM, which transforms the optimization objective into the textitFactual and textitCounterfactual Coverage Maximization to ensure effective radius reduction during data acquisition. Furthermore, benchmarking FCCM against other baselines demonstrates its superiority across both fully synthetic and semi-synthetic datasets.