# A unifying approach for doubly-robust ℓ1 regularized estimation of causal contrasts

arXiv: https://arxiv.org/abs/1904.03737 · HTML: https://mlsanity.com/paper/1904.03737/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Apr 2019.

## Built on by (most cited first, 15 of 15)

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- [Causal inference through multi-stage learning and doubly robust deep neural networks](https://mlsanity.com/paper/2407.08560/) (2024)
- [Normalized Augmented Inverse Probability Weighting with Neural Network Predictions](https://mlsanity.com/paper/2108.01768/) (2021)
- [Treatment Effect Estimation with Observational Network Data using Machine Learning](https://mlsanity.com/paper/2206.14591/) (2022)
- [Efficient estimation of weighted cumulative treatment effects by double/debiased machine learning](https://mlsanity.com/paper/2305.02373/) (2023)
- [Incorporating External Controls for Estimating the Average Treatment Effect on the Treated with High-Dimensional Data: Retaining Double Robustness and Ensuring Double Safety](https://mlsanity.com/paper/2509.20586/) (2025)

## Abstract (arXiv)

We consider inference about a scalar parameter under a non-parametric model based on a one-step estimator computed as a plug in estimator plus the empirical mean of an estimator of the parameter's influence function. We focus on a class of parameters that have influence function which depends on two infinite dimensional nuisance functions and such that the bias of the one-step estimator of the parameter of interest is the expectation of the product of the estimation errors of the two nuisance functions. Our class includes many important treatment effect contrasts of interest in causal inference and econometrics, such as ATE, ATT, an integrated causal contrast with a continuous treatment, and the mean of an outcome missing not at random. We propose estimators of the target parameter that entertain approximately sparse regression models for the nuisance functions allowing for the number of potential confounders to be even larger than the sample size. By employing sample splitting, cross-fitting and ℓ1-regularized regression estimators of the nuisance functions based on objective functions whose directional derivatives agree with those of the parameter's influence function, we obtain estimators of the target parameter with two desirable robustness properties: (1) they are rate doubly-robust in that they are root-n consistent and asymptotically normal when both nuisance functions follow approximately sparse models, even if one function has a very non-sparse regression coefficient, so long as the other has a sufficiently sparse regression coefficient, and (2) they are model doubly-robust in that they are root-n consistent and asymptotically normal even if one of the nuisance functions does not follow an approximately sparse model so long as the other nuisance function follows an approximately sparse model with a sufficiently sparse regression coefficient.