# Meta-learning for heterogeneous treatment effect estimation with closed-form solvers

arXiv: https://arxiv.org/abs/2305.11353 · HTML: https://mlsanity.com/paper/2305.11353/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 46 references that are in the map.
- First posted on arXiv 19 May 2023.

## Builds on (most cited first, 26 of 26)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Prototypical Networks for Few-shot Learning](https://mlsanity.com/paper/1703.05175/) (2017)
- [Matching Networks for One Shot Learning](https://mlsanity.com/paper/1606.04080/) (2016)
- [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)
- [Meta-learning with differentiable closed-form solvers](https://mlsanity.com/paper/1805.08136/) (2018)
- [Learning Representations for Counterfactual Inference](https://mlsanity.com/paper/1605.03661/) (2016)
- [A Survey on Causal Inference](https://mlsanity.com/paper/2002.02770/) (2020)
- [Bayesian Inference of Individualized Treatment Effects using Multi-task Gaussian Processes](https://mlsanity.com/paper/1704.02801/) (2017)
- [A Meta-Transfer Objective for Learning to Disentangle Causal Mechanisms](https://mlsanity.com/paper/1901.10912/) (2019)
- [Estimating Counterfactual Treatment Outcomes over Time Through Adversarially Balanced Representations](https://mlsanity.com/paper/2002.04083/) (2020)
- [Nonparametric Estimation of Heterogeneous Treatment Effects: From Theory to Learning Algorithms](https://mlsanity.com/paper/2101.10943/) (2021)
- [Learning Neural Causal Models from Unknown Interventions](https://mlsanity.com/paper/1910.01075/) (2019)
- [A Survey of Deep Meta-Learning](https://mlsanity.com/paper/2010.03522/) (2020)
- [Learning Weighted Representations for Generalization Across Designs](https://mlsanity.com/paper/1802.08598/) (2018)
- [Invariant Representation Learning for Treatment Effect Estimation](https://mlsanity.com/paper/2011.12379/) (2020)
- [Transfer Learning on Heterogeneous Feature Spaces for Treatment Effects Estimation](https://mlsanity.com/paper/2210.06183/) (2022)
- [Meta Learning for Causal Direction](https://mlsanity.com/paper/2007.02809/) (2020)
- [Transfer Learning for Estimating Causal Effects using Neural Networks](https://mlsanity.com/paper/1808.07804/) (2018)
- [MetaCI: Meta-Learning for Causal Inference in a Heterogeneous Population](https://mlsanity.com/paper/1912.03960/) (2019)
- [Multi-Task Adversarial Learning for Treatment Effect Estimation in Basket Trials](https://mlsanity.com/paper/2203.05123/) (2022)
- [Assessment of Heterogeneous Treatment Effect Estimation Accuracy via Matching](https://mlsanity.com/paper/2003.03881/) (2020)
- [Selecting Treatment Effects Models for Domain Adaptation Using Causal Knowledge](https://mlsanity.com/paper/2102.06271/) (2021)
- [Few-shot Learning for Spatial Regression](https://mlsanity.com/paper/2010.04360/) (2020)

## Built on by (most cited first, 2 of 2)

- [Foundation Models for Causal Inference via Prior-Data Fitted Networks](https://mlsanity.com/paper/2506.10914/) (2025)
- [Moment Matters: Mean and Variance Causal Graph Discovery from Heteroscedastic Observational Data](https://mlsanity.com/paper/2602.23602/) (2026)

## Abstract (arXiv)

This article proposes a meta-learning method for estimating the conditional average treatment effect (CATE) from a few observational data. The proposed method learns how to estimate CATEs from multiple tasks and uses the knowledge for unseen tasks. In the proposed method, based on the meta-learner framework, we decompose the CATE estimation problem into sub-problems. For each sub-problem, we formulate our estimation models using neural networks with task-shared and task-specific parameters. With our formulation, we can obtain optimal task-specific parameters in a closed form that are differentiable with respect to task-shared parameters, making it possible to perform effective meta-learning. The task-shared parameters are trained such that the expected CATE estimation performance in few-shot settings is improved by minimizing the difference between a CATE estimated with a large amount of data and one estimated with just a few data. Our experimental results demonstrate that our method outperforms the existing meta-learning approaches and CATE estimation methods.