# Orthogonal Machine Learning: Power and Limitations

arXiv: https://arxiv.org/abs/1711.00342 · HTML: https://mlsanity.com/paper/1711.00342/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Nov 2017.

## Built on by (most cited first, 28 of 28)

- [Outside the Echo Chamber: Optimizing the Performative Risk](https://mlsanity.com/paper/2102.08570/) (2021)
- [Multi-Task Reinforcement Learning with Mixture of Orthogonal Experts](https://mlsanity.com/paper/2311.11385/) (2023)
- [Deeply-Debiased Off-Policy Interval Estimation](https://mlsanity.com/paper/2105.04646/) (2021)
- [Applied Causal Inference Powered by ML and AI](https://mlsanity.com/paper/2403.02467/) (2024)
- [Doubly-Valid/Doubly-Sharp Sensitivity Analysis for Causal Inference with Unmeasured Confounding](https://mlsanity.com/paper/2112.11449/) (2021)
- [DoubleML -- An Object-Oriented Implementation of Double Machine Learning in Python](https://mlsanity.com/paper/2104.03220/) (2021)
- [Partial Identification with Noisy Covariates: A Robust Optimization Approach](https://mlsanity.com/paper/2202.10665/) (2022)
- [Mitigating Adversarial Vulnerability through Causal Parameter Estimation by Adversarial Double Machine Learning](https://mlsanity.com/paper/2307.07250/) (2023)
- [Off-policy estimation of linear functionals: Non-asymptotic theory for semi-parametric efficiency](https://mlsanity.com/paper/2209.13075/) (2022)
- [Learning Decision Policies with Instrumental Variables through Double Machine Learning](https://mlsanity.com/paper/2405.08498/) (2024)
- [Differentially Private Learners for Heterogeneous Treatment Effects](https://mlsanity.com/paper/2503.03486/) (2025)
- [Coordinated Double Machine Learning](https://mlsanity.com/paper/2206.00885/) (2022)
- [Language Models as Causal Effect Generators](https://mlsanity.com/paper/2411.08019/) (2024)
- [Near Optimal Heteroscedastic Regression with Symbiotic Learning](https://mlsanity.com/paper/2306.14288/) (2023)
- [Orthogonal Statistical Learning with Self-Concordant Loss](https://mlsanity.com/paper/2205.00350/) (2022)
- [Robust Causal Learning for the Estimation of Average Treatment Effects](https://mlsanity.com/paper/2209.01805/) (2022)
- [Covariance alignment: from maximum likelihood estimation to Gromov-Wasserstein](https://mlsanity.com/paper/2311.13595/) (2023)
- [De-paradox Tree: Breaking Down Simpson's Paradox via A Kernel-Based Partition Algorithm](https://mlsanity.com/paper/2603.02174/) (2026)
- [MEC: Machine-Learning-Assisted Generalized Entropy Calibration for Semi-Supervised Mean Estimation](https://mlsanity.com/paper/2604.05446/) (2026)
- [Robust Orthogonal Machine Learning of Treatment Effects](https://mlsanity.com/paper/2103.11869/) (2021)
- [Machine Learning based Framework for Robust Price-Sensitivity Estimation with Application to Airline Pricing](https://mlsanity.com/paper/2205.01875/) (2022)
- [Semantic Autoencoder and Its Potential Usage for Adversarial Attack](https://mlsanity.com/paper/2205.15592/) (2022)
- [Stable Probability Weighting: Large-Sample and Finite-Sample Estimation and Inference Methods for Heterogeneous Causal Effects of Multivalued Treatments Under Limited Overlap](https://mlsanity.com/paper/2301.05703/) (2023)
- [Estimating Treatment Effects with Independent Component Analysis](https://mlsanity.com/paper/2507.16467/) (2025)
- [The Unified Non-Convex Framework for Robust Causal Inference: Overcoming the Gaussian Barrier and Optimization Fragility](https://mlsanity.com/paper/2511.19284/) (2025)
- [Adaptive Estimation and Inference in Semi-parametric Heterogeneous Clustered Multitask Learning via Neyman Orthogonality](https://mlsanity.com/paper/2605.01907/) (2026)
- [ORTHOBO: Orthogonal Bayesian Hyperparameter Optimization](https://mlsanity.com/paper/2605.06454/) (2026)
- [Sharp Structure-Agnostic Minimax Risk for Partial Linear Models](https://mlsanity.com/paper/2609.07997/) (2026)

## Abstract (arXiv)

Double machine learning provides √n-consistent estimates of parameters of interest even when high-dimensional or nonparametric nuisance parameters are estimated at an n-1/4 rate. The key is to employ Neyman-orthogonal moment equations which are first-order insensitive to perturbations in the nuisance parameters. We show that the n-1/4 requirement can be improved to n-1/(2k+2) by employing a k-th order notion of orthogonality that grants robustness to more complex or higher-dimensional nuisance parameters. In the partially linear regression setting popular in causal inference, we show that we can construct second-order orthogonal moments if and only if the treatment residual is not normally distributed. Our proof relies on Stein's lemma and may be of independent interest. We conclude by demonstrating the robustness benefits of an explicit doubly-orthogonal estimation procedure for treatment effect.