# Automatic Debiased Machine Learning for Smooth Functionals of Nonparametric M-Estimands

arXiv: https://arxiv.org/abs/2501.11868 · HTML: https://mlsanity.com/paper/2501.11868/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 84 references that are in the map.
- First posted on arXiv 21 Jan 2025.

## Builds on (most cited first, 28 of 28)

- [Quasi-Oracle Estimation of Heterogeneous Treatment Effects](https://mlsanity.com/paper/1712.04912/) (2017)
- [Orthogonal Statistical Learning](https://mlsanity.com/paper/1901.09036/) (2019)
- [Balancing Covariates via Propensity Score Weighting](https://mlsanity.com/paper/1609.07494/) (2016)
- [Deep Neural Networks for Estimation and Inference](https://mlsanity.com/paper/1809.09953/) (2018)
- [The Influence Function of Semiparametric Estimators](https://mlsanity.com/paper/1508.01378/) (2015)
- [Machine Learning Estimation of Heterogeneous Treatment Effects with Instruments](https://mlsanity.com/paper/1905.10176/) (2019)
- [Long Story Short: Omitted Variable Bias in Causal Machine Learning](https://mlsanity.com/paper/2112.13398/) (2021)
- [Augmented balancing weights as linear regression](https://mlsanity.com/paper/2304.14545/) (2023)
- [The Balancing Act in Causal Inference](https://mlsanity.com/paper/2110.14831/) (2021)
- [Combining T-learning and DR-learning: a framework for oracle-efficient estimation of causal contrasts](https://mlsanity.com/paper/2402.01972/) (2024)
- [Causal isotonic calibration for heterogeneous treatment effects](https://mlsanity.com/paper/2302.14011/) (2023)
- [Automatic Debiased Machine Learning for Covariate Shifts](https://mlsanity.com/paper/2307.04527/) (2023)
- [Efficient Estimation of Pathwise Differentiable Target Parameters with the Undersmoothed Highly Adaptive Lasso](https://mlsanity.com/paper/1908.05607/) (2019)
- [One-Step Estimation of Differentiable Hilbert-Valued Parameters](https://mlsanity.com/paper/2303.16711/) (2023)
- [Simplifying debiased inference via automatic differentiation and probabilistic programming](https://mlsanity.com/paper/2405.08675/) (2024)
- [Source Condition Double Robust Inference on Functionals of Inverse Problems](https://mlsanity.com/paper/2307.13793/) (2023)
- [Stabilized Inverse Probability Weighting via Isotonic Calibration](https://mlsanity.com/paper/2411.06342/) (2024)
- [Median Optimal Treatment Regimes](https://mlsanity.com/paper/2103.01802/) (2021)
- [Proximal Causal Learning of Conditional Average Treatment Effects](https://mlsanity.com/paper/2301.10913/) (2023)
- [Adaptive debiased machine learning using data-driven model selection techniques](https://mlsanity.com/paper/2307.12544/) (2023)
- [Adaptive-TMLE for the Average Treatment Effect based on Randomized Controlled Trial Augmented with Real-World Data](https://mlsanity.com/paper/2405.07186/) (2024)
- [Regularized Orthogonal Machine Learning for Nonlinear Semiparametric Models](https://mlsanity.com/paper/1806.04823/) (2018)
- [Orthogonal Causal Calibration](https://mlsanity.com/paper/2406.01933/) (2024)
- [RieszBoost: Gradient Boosting for Riesz Regression](https://mlsanity.com/paper/2501.04871/) (2025)
- [Universal sieve-based strategies for efficient estimation using machine learning tools](https://mlsanity.com/paper/2003.01856/) (2020)
- [Forster-Warmuth Counterfactual Regression: A Unified Learning Approach](https://mlsanity.com/paper/2307.16798/) (2023)
- [Why Machine Learning Cannot Ignore Maximum Likelihood Estimation](https://mlsanity.com/paper/2110.12112/) (2021)
- [Beta Survival Models](https://mlsanity.com/paper/1905.03818/) (2019)

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

- [Calibeating Prediction-Powered Inference](https://mlsanity.com/paper/2604.21260/) (2026)
- [Efficient Inference for Inverse Reinforcement Learning and Dynamic Discrete Choice Models](https://mlsanity.com/paper/2512.24407/) (2025)
- [Debiased neural operators for estimating functionals](https://mlsanity.com/paper/2604.19296/) (2026)
- [Targeted Deep Architectures: A TMLE-Based Framework for Robust Causal Inference in Neural Networks](https://mlsanity.com/paper/2507.12435/) (2025)
- [Kernel Debiased Plug-in Estimation based on the Universal Least Favorable Submodel](https://mlsanity.com/paper/2603.08945/) (2026)
- [Semiparametric Efficient Bilevel Gradient Estimation](https://mlsanity.com/paper/2605.21341/) (2026)
- [Debiased Machine Learning: Identification, Estimation, and Shape Constraints](https://mlsanity.com/paper/2607.24472/) (2026)

## Abstract (arXiv)

We develop a unified framework for automatic debiased machine learning (autoDML) for inference on a broad class of statistical parameters. The framework applies to any smooth functional of a nonparametric M-estimand, defined as the minimizer of a population risk over an infinite-dimensional linear space. Examples include counterfactual regression, quantile, and survival functions, as well as conditional average treatment effects. Rather than requiring manual derivation of influence functions, our approach automates the construction of debiased estimators using three ingredients: the gradient and Hessian of the loss function and a linear approximation of the target functional. Estimation reduces to solving two risk minimization problems, one for the M-estimand and one for a Riesz representer. The framework accommodates Neyman-orthogonal loss functions that depend on nuisance parameters and extends to vector-valued M-estimands through joint risk minimization. We characterize the efficient influence function and construct efficient autoDML estimators via one-step correction, targeted minimum loss estimation, and sieve-based plug-in methods. Under quadratic risk, these estimators satisfy double robustness for linear functionals. We further show that they are robust to mild misspecification of the M-estimand model, incurring only second-order bias. We illustrate the method by estimating long-term survival probabilities under a semiparametric two-parameter beta-geometric failure model.