= Double machine learning
{wiki}
<Double machine learning> combines <Neyman orthogonality> with <cross-fitting> to estimate a low-dimensional <statistical parameter> while using machine learning for <nuisance function>[nuisance functions]. Orthogonality <mean>[means] that the expected estimating score has zero first <derivative> with respect to nuisance perturbations at the truth. Small nuisance errors therefore affect the target equation only at second order, under the required smoothness assumptions. <cross-fitting> separately limits overfitting effects by evaluating scores on observations excluded from their nuisance training.
For the <augmented inverse-probability-weighted estimator>, a typical sufficient condition is
$$
\|\widehat m-m\|_{L^2}\,\|\widehat e-e\|_{L^2}=o_p(n^{-1/2}),
$$
together with nuisance consistency, suitable <moments> and treatment <probability>[probabilities] bounded away from zero and one. Each error being $o_p(n^{-1/4})$ is sufficient for this product condition, but one may converge more slowly if the other converges faster. Under the full regularity conditions the target estimate has <asymptotic normality> at scale $n^{-1/2}$, enabling <confidence interval>[confidence intervals]. Machine learning prediction accuracy alone does not supply these assumptions or <Causal identification>.<Double Debiased Machine Learning for Treatment and Structural Parameters by Victor Chernozhukov and others>[arXiv v6, Sections 2–3, orthogonality and equation (3.8); Section 5.1, Theorem 5.1]{ref}
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