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Causal Inference Under Unmeasured Confounding With Negative Controls: A Minimax Learning Approach

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arxiv 2103.14029 v4 pith:BFLXE6ZT submitted 2021-03-25 stat.ML cs.LGstat.ME

Nathan Kallus , Xiaojie Mao , Masatoshi Uehara This is my paper
classification stat.MLcs.LGstat.ME
keywords functionsestimationbridgecausalcontrolsidentificationnegativeassumptions
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We study the estimation of causal parameters when not all confounders are observed and instead negative controls are available. Recent work has shown how these can enable identification and efficient estimation via two so-called bridge functions. In this paper, we tackle the primary challenge to causal inference using negative controls: the identification and estimation of these bridge functions. Previous work has relied on completeness conditions on these functions to identify the causal parameters and required uniqueness assumptions in estimation, and they also focused on parametric estimation of bridge functions. Instead, we provide a new identification strategy that avoids the completeness condition. And, we provide new estimators for these functions based on minimax learning formulations. These estimators accommodate general function classes such as Reproducing Kernel Hilbert Spaces and neural networks. We study finite-sample convergence results both for estimating bridge functions themselves and for the final estimation of the causal parameter under a variety of combinations of assumptions. We avoid uniqueness conditions on the bridge functions as much as possible.

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Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Proximal Mediation Analysis with Unmeasured Treatment-Induced Confounding

    stat.ME 2026-07 conditional novelty 7.0 of 10

    Interventional mediation effects are identifiable under unmeasured treatment-induced confounding given two valid proxies, via four proximal formulas and a multiply robust, locally efficient estimator.

  2. Proximal Mediation Analysis with Hidden Recanting Witnesses

    stat.ME 2026-06 conditional novelty 7.0 of 10

    Proposes proximal identification strategies and a multiply robust semiparametric estimator for mediation effects with hidden recanting witnesses.

  3. Decision-Aware Proximal Bridge Learning for Optimal Treatment Selection

    cs.LG 2026-05 unverdicted novelty 7.0 of 10

    Introduces decision-aware proximal bridge learning using a weighted loss and regret bound to enhance optimal treatment selection in settings with hidden confounding.

  4. Proximal Path-Specific Inference

    stat.ME 2026-05 unverdicted novelty 7.0 of 10

    Proximal confounding bridge functions yield four nonparametric identification strategies and a quadruply robust estimator for path-specific effects under unmeasured confounding.

  5. Source-Condition Analysis of Kernel Adversarial Estimators

    math.ST 2025-08 unverdicted novelty 5.0 of 10

    A statistics abstract about finite-sample bounds for kernel adversarial estimators is joined in the submission to the complete text of a different astronomy paper, so the claimed results have no supporting body.

  6. Adaptive Proximal Causal Inference with Some Invalid Proxies

    stat.ME 2025-07 conditional novelty 4.0 of 10

    Using LASSO-style penalties and a median trick over candidate proxies, the paper estimates causal effects when some treatment and outcome proxies violate exclusion restrictions.

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