# Estimating Causal Effects using a Multi-task Deep Ensemble

arXiv: https://arxiv.org/abs/2301.11351 · HTML: https://mlsanity.com/paper/2301.11351/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 44 references that are in the map.
- First posted on arXiv 26 Jan 2023.

## Builds on (most cited first, 17 of 17)

- [Deep Neural Networks as Gaussian Processes](https://mlsanity.com/paper/1711.00165/) (2017)
- [Meta-learners for Estimating Heterogeneous Treatment Effects using Machine Learning](https://mlsanity.com/paper/1706.03461/) (2017)
- [Age Progression/Regression by Conditional Adversarial Autoencoder](https://mlsanity.com/paper/1702.08423/) (2017)
- [Causal Effect Inference with Deep Latent-Variable Models](https://mlsanity.com/paper/1705.08821/) (2017)
- [Learning Representations for Counterfactual Inference](https://mlsanity.com/paper/1605.03661/) (2016)
- [Gaussian Process Behaviour in Wide Deep Neural Networks](https://mlsanity.com/paper/1804.11271/) (2018)
- [Bayesian Inference of Individualized Treatment Effects using Multi-task Gaussian Processes](https://mlsanity.com/paper/1704.02801/) (2017)
- [Deep Convolutional Networks as shallow Gaussian Processes](https://mlsanity.com/paper/1808.05587/) (2018)
- [Automated versus do-it-yourself methods for causal inference: Lessons learned from a data analysis competition](https://mlsanity.com/paper/1707.02641/) (2017)
- [COVID-19 Image Data Collection: Prospective Predictions Are the Future](https://mlsanity.com/paper/2006.11988/) (2020)
- [Bayesian Deep Ensembles via the Neural Tangent Kernel](https://mlsanity.com/paper/2007.05864/) (2020)
- [Deep Counterfactual Networks with Propensity-Dropout](https://mlsanity.com/paper/1706.05966/) (2017)
- [A Critical Look at the Consistency of Causal Estimation With Deep Latent Variable Models](https://mlsanity.com/paper/2102.06648/) (2021)
- [Estimating Average Treatment Effects via Orthogonal Regularization](https://mlsanity.com/paper/2101.08490/) (2021)
- [Valid Causal Inference with (Some) Invalid Instruments](https://mlsanity.com/paper/2006.11386/) (2020)
- [Deep Multi-Modal Structural Equations For Causal Effect Estimation With Unstructured Proxies](https://mlsanity.com/paper/2203.09672/) (2022)
- [Incorporating Prior Knowledge into Neural Networks through an Implicit Composite Kernel](https://mlsanity.com/paper/2205.07384/) (2022)

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

- [Causal Mediation Analysis with Multi-dimensional and Indirectly Observed Mediators](https://mlsanity.com/paper/2306.07918/) (2023)
- [Causal-StoNet: Causal Inference for High-Dimensional Complex Data](https://mlsanity.com/paper/2403.18994/) (2024)
- [CATE Estimation With Potential Outcome Imputation From Local Regression](https://mlsanity.com/paper/2311.03630/) (2023)
- [Estimating treatment effects from single-arm trials via latent-variable modeling](https://mlsanity.com/paper/2311.03002/) (2023)
- [Observationally Informed Adaptive Causal Experimental Design](https://mlsanity.com/paper/2603.03785/) (2026)
- [Enhancing predictive imaging biomarker discovery through treatment effect analysis](https://mlsanity.com/paper/2406.02534/) (2024)
- [Representation Learning for Sample-Efficient CATE Estimation by Leveraging Multiple Outcomes](https://mlsanity.com/paper/2609.06294/) (2026)

## Abstract (arXiv)

A number of methods have been proposed for causal effect estimation, yet few have demonstrated efficacy in handling data with complex structures, such as images. To fill this gap, we propose Causal Multi-task Deep Ensemble (CMDE), a novel framework that learns both shared and group-specific information from the study population. We provide proofs demonstrating equivalency of CDME to a multi-task Gaussian process (GP) with a coregionalization kernel a priori. Compared to multi-task GP, CMDE efficiently handles high-dimensional and multi-modal covariates and provides pointwise uncertainty estimates of causal effects. We evaluate our method across various types of datasets and tasks and find that CMDE outperforms state-of-the-art methods on a majority of these tasks.