# Optimal use of a black-box learner in semiparametric estimation

arXiv: https://arxiv.org/abs/2607.21541 · HTML: https://mlsanity.com/paper/2607.21541/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 56 references that are in the map.
- First posted on arXiv 23 Jul 2026.

## Builds on (most cited first, 25 of 25)

- [Nonparametric regression using deep neural networks with ReLU activation function](https://mlsanity.com/paper/1708.06633/) (2017)
- [Orthogonal Statistical Learning](https://mlsanity.com/paper/1901.09036/) (2019)
- [Confidence Intervals and Hypothesis Testing for High-Dimensional Regression](https://mlsanity.com/paper/1306.3171/) (2013)
- [Double/Debiased/Neyman Machine Learning of Treatment Effects](https://mlsanity.com/paper/1701.08687/) (2017)
- [Approximate Residual Balancing: De-Biased Inference of Average Treatment Effects in High Dimensions](https://mlsanity.com/paper/1604.07125/) (2016)
- [De-biasing the Lasso: Optimal Sample Size for Gaussian Designs](https://mlsanity.com/paper/1508.02757/) (2015)
- [Adversarial Estimation of Riesz Representers](https://mlsanity.com/paper/2101.00009/) (2020)
- [Covariate Balancing Propensity Score by Tailored Loss Functions](https://mlsanity.com/paper/1601.05890/) (2016)
- [De-Biased Machine Learning of Global and Local Parameters Using Regularized Riesz Representers](https://mlsanity.com/paper/1802.08667/) (2018)
- [Augmented Minimax Linear Estimation](https://mlsanity.com/paper/1712.00038/) (2017)
- [Factor Augmented Sparse Throughput Deep ReLU Neural Networks for High Dimensional Regression](https://mlsanity.com/paper/2210.02002/) (2022)
- [How do noise tails impact on deep ReLU networks?](https://mlsanity.com/paper/2203.10418/) (2022)
- [Augmented balancing weights as linear regression](https://mlsanity.com/paper/2304.14545/) (2023)
- [Robust Estimation of Causal Effects via High-Dimensional Covariate Balancing Propensity Score](https://mlsanity.com/paper/1812.08683/) (2018)
- [The Fundamental Limits of Structure-Agnostic Functional Estimation](https://mlsanity.com/paper/2305.04116/) (2023)
- [Debiased Inverse Propensity Score Weighting for Estimation of Average Treatment Effects with High-Dimensional Confounders](https://mlsanity.com/paper/2011.08661/) (2020)
- [Doubly robust inference via calibration](https://mlsanity.com/paper/2411.02771/) (2024)
- [Minimax Semiparametric Learning With Approximate Sparsity](https://mlsanity.com/paper/1912.12213/) (2019)
- [Causality Pursuit from Heterogeneous Environments via Neural Adversarial Invariance Learning](https://mlsanity.com/paper/2405.04715/) (2024)
- [Doubly-robust inference and optimality in structure-agnostic models with smoothness](https://mlsanity.com/paper/2405.08525/) (2024)
- [Optimal Covariate Balancing Conditions in Propensity Score Estimation](https://mlsanity.com/paper/2108.01255/) (2021)
- [It's Hard to Be Normal: The Impact of Noise on Structure-agnostic Estimation](https://mlsanity.com/paper/2507.02275/) (2025)
- [Challenges of the inconsistency regime: Novel debiasing methods for missing data models](https://mlsanity.com/paper/2309.01362/) (2023)
- [Testability of high-dimensional linear models with non-sparse structures](https://mlsanity.com/paper/1802.09117/) (2018)
- [Optimally taming biases in black-box models for efficient semiparametric estimation](https://mlsanity.com/paper/2606.06368/) (2026)

## Built on by (most cited first, 1 of 1)

- [Sharp Structure-Agnostic Minimax Risk for Partial Linear Models](https://mlsanity.com/paper/2609.07997/) (2026)

## Abstract (arXiv)

Consider the partial linear model Y = μ0(X) + β0 · T + varepsilon and T = π0(X) + u in the structure-agnostic setting, where we are blind to the structure μ0 and π0 and estimate the nuisances by a black-box hypothesis class. The learnability of the class is characterized by the estimation error δs in the absence of model misspecification and its L2 mis-specification error δa, μ and δa, π for μ0 and π0, respectively. We propose a novel estimator of the target linear coefficient θ0 = β0 with error rate [ frac1√n + δa, μ · δa, π + [δs]2. ] A matching lower bound is also established, implying that this rate is unimprovable. Compared with the product rate yielded by double machine learning (DML), our estimator removes the suboptimal term max(δa, μ, δa, π)· δs at no extra cost or assumption. Building on the underlying insights, which are neither tailored to the one-learner setting nor the partial linear model, we propose Transductive Adversarial Moment-calibrated Editing (TAME), which locally edits debiasing weights induced by black-box regression estimates on the inference sample through adversarial conditional moment calibration. TAME can be combined with any initial black-box estimates and can strictly improve on DML guarantees when the nuisance difficulties are imbalanced. We discuss how to fully exploit the advantages introduced by TAME, including the gains from using two learners, the resulting under-smoothing principle for model selection, and extensions to other linear functional estimation problems.