Double/De-Biased Machine Learning of Global and Local Parameters Using Regularized Riesz Representers

By Victor Chernozhukov, Whitney K. Newey, Rahul Singh. 2018

113 citations recorded by the source corpus.

We provide adaptive inference methods, based on l1 regularization methods, for regular (semi-parametric) and non-regular (nonparametric) linear functionals of the conditional expectation function. Examples of regular functionals include average treatment effects, policy effects from covariate distribution shifts and stochastic transformations, and average derivatives. Examples of non-regular functionals include the local linear functionals defined as local averages that approximate perfectly localized quantities: average treatment, average policy effects, and average derivatives, conditional on a covariate subvector fixed at a point. Our construction relies on building Neyman orthogonal equations for the target parameter that are approximately invariant to small perturbations of the nuisance parameters. To achieve this property we include the linear Riesz representer for the functionals in the equations as the additional nuisance parameter. We use l1-regularized methods to learn approximations to the regression function and the linear representer, in settings where dimension of (possibly overcomplete) dictionary of basis functions P is much larger than N. We then estimate the linear functional by the solution to the empirical analog of the orthogonal equations. Our key result is that under weak assumptions the estimator of the functional concentrates in a L/root(n) neighborhood of the target with deviations controlled by the Gaussian law, provided L/root(n) \to 0; L is the operator norm of the functional, measuring the degree of its non-regularity, with L diverging for local functionals (or under weak identification of the global functionals).

Subfields: Aerospace Engineering, Radiology, Nuclear Medicine and Imaging, Statistics and Probability, Causal Inference & Discovery, Statistical Learning Theory

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Citations in the corpus

Double Debiased Machine Learning Nonparametric Inference with Continuous Treatments (2019, unknown): “Klosin (2021) and Chernozhukov, Newey, and Singh (2022b) also avoid inverting estimated propensity scores for average treatment effects by directly estimating the reciprocal of the GPS or Riesz representer.”
Long-term Causal Inference Under Persistent Confounding via Data Combination (2022, methodology): “2, we prove that the estimating equation based on the doubly robust identification strategy in Theorem 7 satisfies the Neyman orthogonality property [Chernozhukov et al., 2019], and show that the resulting treatment effect estimator has appealing asymptotic properties.”
Incremental causal effects (2019, methodology): “In Hirshberg and Wager (2017), this is achieved under Donsker assumptions, while Chernozhukov et al. (2018) employ a sparsity assumption on either the approximation of the Riesz representer or the approximation to the regression function.”
A unifying approach for doubly-robust $\ell_1$ regularized estimation of causal contrasts (2019, methodology): “Specifically, Chernozhukov et al. (2018) showed that ATE is an instance of a much larger class of functionals, which includes many parameters of interest in causal inference, and which can be expressed as a continuos and linear functional of the conditional mean of an outcome given covariates.”
Policy Learning With Observational Data (2017, methodology): “…to their ability to achieve semiparametric eﬃciency under general conditions, even if nuisance components are estimated via black-box machine learning methods for which we can only guarantee fast enough convergence in mean-squared error (Chernozhukov et al., 2018a; van der Laan and Rose, 2011).”
Debiased Inference of Average Partial Effects in Single-Index Models (2018, methodology): “…and then debias the plug-in estimator for τj based on θ̂ using a weighted average of residuals:1 τ̂j = 1 n n∑ i=1 ( θ̂jψ ( XTi θ̂ ) + γ̂i ( Yi −Ψ ( XTi θ̂ ))) , (4) 1Our proposed estimator will also use cross-fitting [Chernozhukov et al., 2018a], but we suppress this notation here for conciseness.”
Characterization of parameters with a mixed bias property (2019, methodology): “In the Econometrics literature, Chernozhukov et al. (2018) have shown that parameters of the form χ (η) = Eη [d (O, a)] where a (Z) ≡ Eη (Y |Z) and d (O, a) is such that the map h ∈ L2 (Pη,Z) → Eη [d (O, h)] is a continuous and affine linear, also satisfy the mixed bias property.”