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

TL;DR

This paper introduces a nonasymptotic debiased machine learning theorem that guarantees finite sample validity for confidence intervals of functionals derived from machine learning algorithms, under simple conditions.

Contribution

It provides the first finite sample guarantees for debiased machine learning applicable to any functional and any machine learning method satisfying basic conditions.

Findings

Proves consistency, Gaussian approximation, and efficiency with finite samples.

Achieves a $n^{-1/2}$ convergence rate for global functionals.

Reveals a double robustness property for inverse problems.

Abstract

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.