{"ID":2898569,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.02275","arxiv_id":"2507.02275","title":"It's Hard to Be Normal: The Impact of Noise on Structure-agnostic Estimation","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 \\emph{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.","short_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. Focu...","url_abs":"https://arxiv.org/abs/2507.02275","url_pdf":"https://arxiv.org/pdf/2507.02275v3","authors":"[\"Jikai Jin\",\"Lester Mackey\",\"Vasilis Syrgkanis\"]","published":"2025-07-03T03:31:45Z","proceeding":"stat.ML","tasks":"[\"stat.ML\",\"cs.LG\",\"econ.EM\",\"math.ST\",\"stat.ME\"]","methods":"[]","has_code":false}