# Estimating Average Treatment Effects via Orthogonal Regularization

arXiv: https://arxiv.org/abs/2101.08490 · HTML: https://mlsanity.com/paper/2101.08490/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 70 references that are in the map.
- First posted on arXiv 21 Jan 2021.

## Builds on (most cited first, 16 of 16)

- [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)
- [Quasi-Oracle Estimation of Heterogeneous Treatment Effects](https://mlsanity.com/paper/1712.04912/) (2017)
- [Learning Representations for Counterfactual Inference](https://mlsanity.com/paper/1605.03661/) (2016)
- [Adapting Neural Networks for the Estimation of Treatment Effects](https://mlsanity.com/paper/1906.02120/) (2019)
- [Optimal and Adaptive Off-policy Evaluation in Contextual Bandits](https://mlsanity.com/paper/1612.01205/) (2016)
- [Balanced Policy Evaluation and Learning](https://mlsanity.com/paper/1705.07384/) (2017)
- [Approximate Residual Balancing: De-Biased Inference of Average Treatment Effects in High Dimensions](https://mlsanity.com/paper/1604.07125/) (2016)
- [Benchmarking Framework for Performance-Evaluation of Causal Inference Analysis](https://mlsanity.com/paper/1802.05046/) (2018)
- [Matching in Selective and Balanced Representation Space for Treatment Effects Estimation](https://mlsanity.com/paper/2009.06828/) (2020)
- [Recursive Partitioning for Personalization using Observational Data](https://mlsanity.com/paper/1608.08925/) (2016)
- [Estimating Individual Treatment Effects with Time-Varying Confounders](https://mlsanity.com/paper/2008.13620/) (2020)
- [Linked Causal Variational Autoencoder for Inferring Paired Spillover Effects](https://mlsanity.com/paper/1808.03333/) (2018)
- [Structural Nested Models and G-estimation: The Partially Realized Promise](https://mlsanity.com/paper/1503.01589/) (2015)
- [Debiased Bayesian inference for average treatment effects](https://mlsanity.com/paper/1909.12078/) (2019)
- [Estimating Average Treatment Effects: Supplementary Analyses and Remaining Challenges](https://mlsanity.com/paper/1702.01250/) (2017)

## Built on by (most cited first, 25 of 25)

- [On Inductive Biases for Heterogeneous Treatment Effect Estimation](https://mlsanity.com/paper/2106.03765/) (2021)
- [Causal Machine Learning for Healthcare and Precision Medicine](https://mlsanity.com/paper/2205.11402/) (2022)
- [Causal Effect Inference for Structured Treatments](https://mlsanity.com/paper/2106.01939/) (2021)
- [Combining Observational and Randomized Data for Estimating Heterogeneous Treatment Effects](https://mlsanity.com/paper/2202.12891/) (2022)
- [Sequential Deconfounding for Causal Inference with Unobserved Confounders](https://mlsanity.com/paper/2104.09323/) (2021)
- [Normalizing Flows for Interventional Density Estimation](https://mlsanity.com/paper/2209.06203/) (2022)
- [DiffPO: A causal diffusion model for learning distributions of potential outcomes](https://mlsanity.com/paper/2410.08924/) (2024)
- [Generalizing Off-Policy Learning under Sample Selection Bias](https://mlsanity.com/paper/2112.01387/) (2021)
- [Deconfounding Temporal Autoencoder: Estimating Treatment Effects over Time Using Noisy Proxies](https://mlsanity.com/paper/2112.03013/) (2021)
- [AttDMM: An Attentive Deep Markov Model for Risk Scoring in Intensive Care Units](https://mlsanity.com/paper/2102.04702/) (2021)
- [Partial Counterfactual Identification of Continuous Outcomes with a Curvature Sensitivity Model](https://mlsanity.com/paper/2306.01424/) (2023)
- [Deep Causal Learning: Representation, Discovery and Inference](https://mlsanity.com/paper/2211.03374/) (2022)
- [A Survey of Deep Causal Models and Their Industrial Applications](https://mlsanity.com/paper/2209.08860/) (2022)
- [Estimating Conditional Average Treatment Effects with Missing Treatment Information](https://mlsanity.com/paper/2203.01422/) (2022)
- [Estimating Causal Effects using a Multi-task Deep Ensemble](https://mlsanity.com/paper/2301.11351/) (2023)
- [Stabilized Neural Prediction of Potential Outcomes in Continuous Time](https://mlsanity.com/paper/2410.03514/) (2024)
- [Causal Machine Learning for Cost-Effective Allocation of Development Aid](https://mlsanity.com/paper/2401.16986/) (2024)
- [Constructing Confidence Intervals for Average Treatment Effects from Multiple Datasets](https://mlsanity.com/paper/2412.11511/) (2024)
- [Causal-StoNet: Causal Inference for High-Dimensional Complex Data](https://mlsanity.com/paper/2403.18994/) (2024)
- [Detecting User Exits from Online Behavior: A Duration-Dependent Latent State Model](https://mlsanity.com/paper/2208.03937/) (2022)
- [Moderately-Balanced Representation Learning for Treatment Effects with Orthogonality Information](https://mlsanity.com/paper/2209.01956/) (2022)
- [A Multi-class Ride-hailing Service Subsidy System Utilizing Deep Causal Networks](https://mlsanity.com/paper/2408.02065/) (2024)
- [Multiple Instance Learning for Uplift Modeling](https://mlsanity.com/paper/2312.09639/) (2023)
- [TSCAN: Context-Aware Uplift Modeling via Two-Stage Training for Online Merchant Business Diagnosis](https://mlsanity.com/paper/2504.18881/) (2025)
- [Deconfounded Warm-Start Thompson Sampling with Applications to Precision Medicine](https://mlsanity.com/paper/2505.17283/) (2025)

## Abstract (arXiv)

Decision-making often requires accurate estimation of treatment effects from observational data. This is challenging as outcomes of alternative decisions are not observed and have to be estimated. Previous methods estimate outcomes based on unconfoundedness but neglect any constraints that unconfoundedness imposes on the outcomes. In this paper, we propose a novel regularization framework for estimating average treatment effects that exploits unconfoundedness. To this end, we formalize unconfoundedness as an orthogonality constraint, which ensures that the outcomes are orthogonal to the treatment assignment. This orthogonality constraint is then included in the loss function via a regularization. Based on our regularization framework, we develop deep orthogonal networks for unconfounded treatments (DONUT), which learn outcomes that are orthogonal to the treatment assignment. Using a variety of benchmark datasets for estimating average treatment effects, we demonstrate that DONUT outperforms the state-of-the-art substantially.