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It's Hard to Be Normal: The Impact of Noise on Structure-agnostic Estimation

Jikai Jin, Lester Mackey, Vasilis Syrgkanis

arXiv 3 Jul 2025 · Statistics — Machine Learning

arXiv:2507.02275 · PDF · Extracted main text

Abstract

Structure-agnostic causal inference studies how well one can estimate a treatment effect given black-box machine learning estimates of nuisance functions (like the impact of confounders on treatment and outcomes). Here, we find that the answer depends in a surprising way on the distribution of the treatment noise. Focusing on the partially linear model of \citet{robinson1988root}, we first show that the widely adopted double machine learning (DML) estimator is minimax rate-optimal for Gaussian treatment noise, resolving an open problem of \citet{mackey2018orthogonal}. Meanwhile, for independent non-Gaussian treatment noise, we show that DML is always suboptimal by constructing new practical procedures with higher-order robustness to nuisance errors. These ACE procedures use structure-agnostic cumulant estimators to achieve $r$-th order insensitivity to nuisance errors whenever the $(r+1)$-st treatment cumulant is non-zero. We complement these core results with novel minimax guarantees for binary treatments in the partially linear model. Finally, using synthetic demand estimation experiments, we demonstrate the practical benefits of our higher-order robust estimators.

Citation extraction

32
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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Sivaraman Balakrishnan, Edward H Kennedy, and Larry Wasserman (2023) The fundamental limits of structure-agnostic functional estimation0.9507486%
2Victor Chernozhukov, Denis Chetverikov, Mert Demirer, Esther Duflo,… (2018) Double/debiased machine learning for treatment and structural parameters: Double/debiased machine learning0.9416583%
3Jikai Jin and Vasilis Syrgkanis (2024) Structure-agnostic optimality of doubly robust learning for treatment effect estimation self0.8746567%
4Lester Mackey, Vasilis Syrgkanis, and Ilias Zadik (2018) Orthogonal machine learning: Power and limitations self0.80523852%
5Victor Chernozhukov, Whitney K Newey, and Rahul Singh (2022) Automatic debiased machine learning of causal and structural effects0.6443267%
6Peter M Robinson (1988) Root-n-consistent semiparametric regression0.64422100%
7T Tony Cai and Mark G Low (2011) Testing composite hypotheses, hermite polynomials and optimal estimation of a nonsmooth functional0.5114225%
8Rick Durrett (2019) Probability: theory and examples, volume 490.5112250%
9Charles J Stone (1982) Optimal global rates of convergence for nonparametric regression0.5112250%
10Alexandre Belloni, Victor Chernozhukov, and Christian Hansen (2011) Inference for high-dimensional sparse econometric models0.40511100%

Showing the top 10 of 32 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Learning bounds for doubly-robust covariate shift adaptation0.64422
2On the Asymptotic Inadmissibility of Double Machine Learning Estimators Under Structure-Agnostic Models0.40511