# A Doubly Robust Machine Learning Approach for Disentangling Treatment Effect Heterogeneity with Functional Outcomes

arXiv: https://arxiv.org/abs/2602.11118 · HTML: https://mlsanity.com/paper/2602.11118/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 56 references that are in the map.
- First posted on arXiv 11 Feb 2026.

## Builds on (most cited first, 19 of 19)

- [Multimodal Deep Learning](https://mlsanity.com/paper/2301.04856/) (2023)
- [Semiparametric doubly robust targeted double machine learning: a review](https://mlsanity.com/paper/2203.06469/) (2022)
- [Multimodal learning with graphs](https://mlsanity.com/paper/2209.03299/) (2022)
- [Learning Interpretable Concepts: Unifying Causal Representation Learning and Foundation Models](https://mlsanity.com/paper/2402.09236/) (2024)
- [Estimating Individual Treatment Effects using Non-Parametric Regression Models: a Review](https://mlsanity.com/paper/2009.06472/) (2020)
- [Deep Learning for Functional Data Analysis with Adaptive Basis Layers](https://mlsanity.com/paper/2106.10414/) (2021)
- [Non-linear Functional Modeling using Neural Networks](https://mlsanity.com/paper/2104.09371/) (2021)
- [Modern Non-Linear Function-on-Function Regression](https://mlsanity.com/paper/2107.14151/) (2021)
- [Causal inference with a functional outcome](https://mlsanity.com/paper/2304.07113/) (2023)
- [An Introduction to Double/Debiased Machine Learning](https://mlsanity.com/paper/2504.08324/) (2025)
- [Optimal Individualized Treatment Rule for Combination Treatments Under Budget Constraints](https://mlsanity.com/paper/2303.11507/) (2023)
- [FAStEN: An Efficient Adaptive Method for Feature Selection and Estimation in High-Dimensional Functional Regressions](https://mlsanity.com/paper/2303.14801/) (2023)
- [Doubly-Robust Functional Average Treatment Effect Estimation](https://mlsanity.com/paper/2501.06024/) (2025)
- [Kernel-based estimators for functional causal effects](https://mlsanity.com/paper/2503.05024/) (2025)
- [Causal Effect of Functional Treatment](https://mlsanity.com/paper/2210.00242/) (2022)
- [A new computationally efficient algorithm to solve Feature Selection for Functional Data Classification in high-dimensional spaces](https://mlsanity.com/paper/2401.05765/) (2024)
- [Venture Capital investments through the lens of Network and Functional Data Analysis](https://mlsanity.com/paper/2202.12859/) (2022)
- [Functional Graph Convolutional Networks: A unified multi-task and multi-modal learning framework to facilitate health and social-care insights](https://mlsanity.com/paper/2403.10158/) (2024)
- [Doubly robust estimation with functional outcomes missing at random](https://mlsanity.com/paper/2411.17224/) (2024)

## Built on by (most cited first, 1 of 1)

- [Bayesian X-Learner: Calibrated Posterior Inference for Heterogeneous Treatment Effects under Heavy-Tailed Outcomes](https://mlsanity.com/paper/2604.27394/) (2026)

## Abstract (arXiv)

Causal inference is paramount for understanding the effects of interventions, yet extracting personalized insights from increasingly complex data remains a significant challenge for modern machine learning. This is the case, in particular, when considering functional outcomes observed over a continuous domain (e.g., time, or space). Estimation of heterogeneous treatment effects, known as CATE, has emerged as a crucial tool for personalized decision-making, but existing meta-learning frameworks are largely limited to scalar outcomes, failing to provide satisfying results in scientific applications that leverage the rich, continuous information encoded in functional data. Here, we introduce FOCaL (Functional Outcome Causal Learning), a novel, doubly robust meta-learner specifically engineered to estimate a functional heterogeneous treatment effect (F-CATE). FOCaL integrates advanced functional regression techniques for both outcome modeling and functional pseudo-outcome reconstruction, thereby enabling the direct and robust estimation of F-CATE. We provide a rigorous theoretical derivation of FOCaL, demonstrate its performance and robustness compared to existing non-robust functional methods through comprehensive simulation studies, and illustrate its practical utility on diverse real-world functional datasets. FOCaL advances the capabilities of machine intelligence to infer nuanced, individualized causal effects from complex data, paving the way for more precise and trustworthy AI systems in personalized medicine, adaptive policy design, and fundamental scientific discovery.