Automatic doubly robust inference for linear functionals via calibrated debiased machine learning

2024-11-05

AI Summary

Doubly robust (DR) estimators are widely used for linear functionals such as the average treatment effect, but their asymptotic normality typically requires both nuisance functions to converge at sufficiently fast rates—stricter than the consistency condition requiring only one nuisance function to be consistent. Method: This paper proposes Calibrated Debiased Machine Learning (C-DML), a novel framework that establishes, for the first time, a theoretical connection between calibration techniques and doubly robust asymptotic linearity. C-DML constructs a calibration loss via the Riesz representer, integrating cross-fitting, isotonic calibration, and the bootstrap to achieve robust nuisance estimation. Contribution/Results: We prove that C-DML achieves both double robustness and asymptotic normality under minimal rate conditions. Empirically, it maintains high-coverage confidence intervals even when one nuisance model is misspecified or converges slowly, substantially reducing estimation bias compared to standard DR approaches.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Causality
• Intelligent Robots: State Estimation

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

In causal inference, many estimands of interest can be expressed as a linear functional of the outcome regression function; this includes, for example, average causal effects of static, dynamic and stochastic interventions. For learning such estimands, in this work, we propose novel debiased machine learning estimators that are doubly robust asymptotically linear, thus providing not only doubly robust consistency but also facilitating doubly robust inference (e.g., confidence intervals and hypothesis tests). To do so, we first establish a key link between calibration, a machine learning technique typically used in prediction and classification tasks, and the conditions needed to achieve doubly robust asymptotic linearity. We then introduce calibrated debiased machine learning (C-DML), a unified framework for doubly robust inference, and propose a specific C-DML estimator that integrates cross-fitting, isotonic calibration, and debiased machine learning estimation. A C-DML estimator maintains asymptotic linearity when either the outcome regression or the Riesz representer of the linear functional is estimated sufficiently well, allowing the other to be estimated at arbitrarily slow rates or even inconsistently. We propose a simple bootstrap-assisted approach for constructing doubly robust confidence intervals. Our theoretical and empirical results support the use of C-DML to mitigate bias arising from the inconsistent or slow estimation of nuisance functions.

Problem

• Achieving doubly robust asymptotic normality via calibration
• Enhancing inference with calibrated debiased machine learning
• Improving coverage and bias in treatment effect estimation

Innovation

• Calibrated DML ensures doubly robust normality
• Isotonic regression adjusts standard DML estimates
• Bootstrap enables robust confidence intervals simply