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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 seek the confidence interval for a treatment effect estimated with a neural network. We present a non-asymptotic 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. 

Multi-dimensional heterogeneity and endogeneity are important features of models with multiple treatments. We consider a heterogeneous coefficients model where the outcome is a linear combination of dummy treatment variables, with each variable representing a different kind of treatment. We use control variables to give necessary and sufficient conditions for identification of average treatment effects. With mutually exclusive treatments we find that, provided the heterogeneous coefficients are mean independent from treatments given the controls, a simple identification condition is that the generalized propensity scores (Imbens, 2000) be bounded away from zero and that their sum be bounded away from one, with probability one. Our analysis extends to distributional and quantile treatment effects, as well as corresponding treatment effects on the treated. These results generalize the classical identification result of Rosenbaum & Rubin (1983) for binary treatments.