# Selective machine learning of doubly robust functionals

arXiv: https://arxiv.org/abs/1911.02029 · HTML: https://mlsanity.com/paper/1911.02029/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Nov 2019.

## Built on by (most cited first, 9 of 9)

- [In Search of Insights, Not Magic Bullets: Towards Demystification of the Model Selection Dilemma in Heterogeneous Treatment Effect Estimation](https://mlsanity.com/paper/2302.02923/) (2023)
- [Doubly-Valid/Doubly-Sharp Sensitivity Analysis for Causal Inference with Unmeasured Confounding](https://mlsanity.com/paper/2112.11449/) (2021)
- [Minimax Kernel Machine Learning for a Class of Doubly Robust Functionals with Application to Proximal Causal Inference](https://mlsanity.com/paper/2104.02929/) (2021)
- [Validating Causal Inference Methods](https://mlsanity.com/paper/2202.04208/) (2022)
- [DeepMed: Semiparametric Causal Mediation Analysis with Debiased Deep Learning](https://mlsanity.com/paper/2210.04389/) (2022)
- [Adaptive debiased machine learning using data-driven model selection techniques](https://mlsanity.com/paper/2307.12544/) (2023)
- [Optimal Treatment Regimes for Proximal Causal Learning](https://mlsanity.com/paper/2212.09494/) (2022)
- [Unveiling the Potential of Robustness in Selecting Conditional Average Treatment Effect Estimators](https://mlsanity.com/paper/2402.18392/) (2024)
- [Climate Variability Modulates the Impact of Price Spikes on Food Insecurity](https://mlsanity.com/paper/2609.24394/) (2026)

## Abstract (arXiv)

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.