A Simple and General Debiased Machine Learning Theorem with Finite Sample Guarantees
This work addresses the need for reliable statistical inference in machine learning applications, offering a general framework that translates learning theory rates into traditional inference, which is significant for analysts and researchers but appears incremental as it builds on existing debiased ML concepts.
The paper tackles the problem of constructing confidence intervals for functionals of machine learning algorithms, such as treatment effects estimated with neural networks, by providing a nonasymptotic debiased machine learning theorem with finite sample guarantees, achieving a convergence rate of n^{-1/2} for global functionals and graceful degradation for local ones.
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.