Selective machine learning of doubly robust functionals

Abstract

While model selection is a well-studied topic in parametric and nonparametric regression or density estimation, selection of possibly high-dimensional nuisance parameters in semiparametric problems is far less developed. In this paper, we propose a selective machine learning framework for making inferences about a finite-dimensional functional defined on a semiparametric model, when the latter admits a doubly robust estimating function and several candidate machine learning algorithms are available for estimating the nuisance parameters. We introduce a new selection criterion aimed at bias reduction in estimating the functional of interest based on a novel definition of pseudo-risk inspired by the double robustness property. Intuitively, the proposed criterion selects a pair of learners with the smallest pseudo-risk, so that the estimated functional is least sensitive to perturbations of a nuisance parameter. We establish an oracle property for a multi-fold cross-validation version of the new selection criterion which states that our empirical criterion performs nearly as well as an oracle with a priori knowledge of the pseudo-risk for each pair of candidate learners. Finally, we apply the approach to model selection of a semiparametric estimator of average treatment effect given an ensemble of candidate machine learners to account for confounding in an observational study which we illustrate in simulations and a data application.

To appear in Biometrika

References in corpus (4)

• Semiparametric theory for causal mediation analysis: Efficiency bounds, multiple robustness and sensitivity analysis
• Oracle, Multiple Robust and Multipurpose Calibration in a Missing Response Problem
• A unifying approach for doubly-robust ${\ell }_1$ regularized estimation of causal contrasts
• On doubly robust estimation for logistic partially linear models

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• The costs and benefits of uniformly valid causal inference with high-dimensional nuisance parameters
• Selective Machine Learning of the Average Treatment Effect with an Invalid Instrumental Variable
• Generalized interpretation and identification of separable effects in competing event settings
• On nearly assumption-free tests of nominal confidence interval coverage for causal parameters estimated by machine learning
• Regularizing Double Machine Learning in Partially Linear Endogenous Models
• Model selection for estimation of causal parameters
• Double-robust and efficient methods for estimating the causal effects of a binary treatment
• Clinically Relevant Mediation Analysis using Controlled Indirect Effect