A simple and general debiased machine learning theorem with finite-sample guarantees

Victor Chernozhukov, Whitney Newey, Rahul Singh

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.