mlsanityData to 7 Oct 2026

Source Condition Double Robust Inference on Functionals of Inverse Problems

arXiv 2307.13793 ↗First posted 25 Jul 2023stat.ME cs.LG econ.EMcited by 8

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Abstract (arXiv)

We consider estimation of parameters defined as linear functionals of solutions to linear inverse problems. Any such parameter admits a doubly robust representation that depends on the solution to a dual linear inverse problem, where the dual solution can be thought as a generalization of the inverse propensity function. We provide the first source condition double robust inference method that ensures asymptotic normality around the parameter of interest as long as either the primal or the dual inverse problem is sufficiently well-posed, without knowledge of which inverse problem is the more well-posed one. Our result is enabled by novel guarantees for iterated Tikhonov regularized adversarial estimators for linear inverse problems, over general hypothesis spaces, which are developments of independent interest.

Key facts. Cited by 8 papers in the map (data through 7 Oct 2026). Builds on 21 of its 61 references that are in the map. First posted on arXiv 25 Jul 2023.

Builds on

21 of 61 references.

References · 21

  1. 2017The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problemscited by 581
  2. 2019Orthogonal Statistical Learningcited by 150
  3. 2019Kernel Instrumental Variable Regressioncited by 118
  4. 2019Deep Generalized Method of Moments for Instrumental Variable Analysiscited by 88
  5. 2020Minimax Estimation of Conditional Moment Modelscited by 83
  6. 2017Double/Debiased/Neyman Machine Learning of Treatment Effectscited by 76
  7. 2019Off-Policy Evaluation in Partially Observable Environmentscited by 65
  8. 2020Learning Deep Features in Instrumental Variable Regressioncited by 65
  9. 2020Semiparametric proximal causal inferencecited by 58
  10. 2021Causal Inference Under Unmeasured Confounding With Negative Controls: A Minimax Learning Approachcited by 43
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9 more
  1. 2018Adversarial Generalized Method of Momentscited by 34
  2. 2020Adversarial Estimation of Riesz Representerscited by 34
  3. 2020Provably Efficient Neural Estimation of Structural Equation Model: An Adversarial Approachcited by 31
  4. 2020The Variational Method of Momentscited by 23
  5. 2022Off-Policy Evaluation for Episodic Partially Observable Markov Decision Processes under Non-Parametric Modelscited by 18
  6. 2020On Deep Instrumental Variables Estimatecited by 14
  7. 2023Minimax Instrumental Variable Regression and L2 Convergence Guarantees without Identification or Closednesscited by 13
  8. 2021Learning Causal Models from Conditional Moment Restrictions by Importance Weightingcited by 7
  9. 2021Nonparametric inference about mean functionals of nonignorable nonresponse data without identifying the joint distributioncited by 4

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 2; 2025: 4; 2026: 2.

8 papers.

  1. 2024Spectral Representation for Causal Estimation with Hidden Confounderscited by 12
  2. 2024Nonparametric Instrumental Regression via Kernel Methods is Minimax Optimalcited by 7
  3. 2025Automatic Debiased Machine Learning for Smooth Functionals of Nonparametric M-Estimandscited by 5
  4. 2025Optimality and Adaptivity of Deep Neural Features for Instrumental Variable Regressioncited by 3
  5. 2025Detecting clinician implicit biases in diagnoses using proximal causal inferencecited by 1
  6. 2025Learning Treatment Representations for Downstream Instrumental Variable Regressioncited by 0
  7. 2026Adaptive Estimation and Inference in Conditional Moment Models via the Discrepancy Principlecited by 0
  8. 2026Nonparametric Instrumental Variable Analysis Without Structural Equations: Debiased Inference on Functionals of Inverse Problems with No Solutionscited by 0