# A Simple and General Debiased Machine Learning Theorem with Finite Sample Guarantees

arXiv: https://arxiv.org/abs/2105.15197 · HTML: https://mlsanity.com/paper/2105.15197/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 56 references that are in the map.
- First posted on arXiv 31 May 2021.

## Builds on (most cited first, 11 of 11)

- [Orthogonal Statistical Learning](https://mlsanity.com/paper/1901.09036/) (2019)
- [Kernel Instrumental Variable Regression](https://mlsanity.com/paper/1906.00232/) (2019)
- [Minimax Estimation of Conditional Moment Models](https://mlsanity.com/paper/2006.07201/) (2020)
- [Causal Inference Under Unmeasured Confounding With Negative Controls: A Minimax Learning Approach](https://mlsanity.com/paper/2103.14029/) (2021)
- [The Influence Function of Semiparametric Estimators](https://mlsanity.com/paper/1508.01378/) (2015)
- [Adversarial Estimation of Riesz Representers](https://mlsanity.com/paper/2101.00009/) (2020)
- [De-Biased Machine Learning of Global and Local Parameters Using Regularized Riesz Representers](https://mlsanity.com/paper/1802.08667/) (2018)
- [A unifying approach for doubly-robust ℓ1 regularized estimation of causal contrasts](https://mlsanity.com/paper/1904.03737/) (2019)
- [Uniform Post Selection Inference for LAD Regression and Other Z-estimation problems](https://mlsanity.com/paper/1304.0282/) (2013)
- [Universal sieve-based strategies for efficient estimation using machine learning tools](https://mlsanity.com/paper/2003.01856/) (2020)
- [Data-adaptive smoothing for optimal-rate estimation of possibly non-regular parameters](https://mlsanity.com/paper/1706.07408/) (2017)

## Built on by (most cited first, 9 of 9)

- [Cross-Prediction-Powered Inference](https://mlsanity.com/paper/2309.16598/) (2023)
- [Debiased Machine Learning without Sample-Splitting for Stable Estimators](https://mlsanity.com/paper/2206.01825/) (2022)
- [One-Step Estimation of Differentiable Hilbert-Valued Parameters](https://mlsanity.com/paper/2303.16711/) (2023)
- [Structure-agnostic Optimality of Doubly Robust Learning for Treatment Effect Estimation](https://mlsanity.com/paper/2402.14264/) (2024)
- [Learning High-dimensional Gaussians from Censored Data](https://mlsanity.com/paper/2504.19446/) (2025)
- [Generalized Kernel Ridge Regression for Causal Inference with Missing-at-Random Sample Selection](https://mlsanity.com/paper/2111.05277/) (2021)
- [A Meta-Learning Method for Estimation of Causal Excursion Effects to Assess Time-Varying Moderation](https://mlsanity.com/paper/2306.16297/) (2023)
- [Predicting Long Term Sequential Policy Value Using Softer Surrogates](https://mlsanity.com/paper/2412.20638/) (2024)
- [Sharp Structure-Agnostic Minimax Risk for Partial Linear Models](https://mlsanity.com/paper/2609.07997/) (2026)

## Abstract (arXiv)

Debiased machine learning is a meta algorithm based on bias correction and sample splitting to calculate confidence intervals for functionals, i.e. scalar summaries, of machine learning algorithms. For example, an analyst may desire the confidence interval for a treatment effect estimated with a neural network. We provide a nonasymptotic debiased machine learning theorem that encompasses any global or local functional of any machine learning algorithm that satisfies a few simple, interpretable conditions. Formally, we prove consistency, Gaussian approximation, and semiparametric efficiency by finite sample arguments. The rate of convergence is n-1/2 for global functionals, and it degrades gracefully for local functionals. Our results culminate in a simple set of conditions that an analyst can use to translate modern learning theory rates into traditional statistical inference. The conditions reveal a general double robustness property for ill posed inverse problems.