# Automatic debiasing of neural networks via moment-constrained learning

arXiv: https://arxiv.org/abs/2409.19777 · HTML: https://mlsanity.com/paper/2409.19777/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 50 references that are in the map.
- First posted on arXiv 29 Sep 2024.

## Builds on (most cited first, 19 of 19)

- [Adapting Neural Networks for the Estimation of Treatment Effects](https://mlsanity.com/paper/1906.02120/) (2019)
- [Orthogonal Statistical Learning](https://mlsanity.com/paper/1901.09036/) (2019)
- [Equinox: neural networks in JAX via callable PyTrees and filtered transformations](https://mlsanity.com/paper/2111.00254/) (2021)
- [A Unified Analysis of Extra-gradient and Optimistic Gradient Methods for Saddle Point Problems: Proximal Point Approach](https://mlsanity.com/paper/1901.08511/) (2019)
- [Semiparametric doubly robust targeted double machine learning: a review](https://mlsanity.com/paper/2203.06469/) (2022)
- [Minimax Estimation of Conditional Moment Models](https://mlsanity.com/paper/2006.07201/) (2020)
- [Approximate Residual Balancing: De-Biased Inference of Average Treatment Effects in High Dimensions](https://mlsanity.com/paper/1604.07125/) (2016)
- [RieszNet and ForestRiesz: Automatic Debiased Machine Learning with Neural Nets and Random Forests](https://mlsanity.com/paper/2110.03031/) (2021)
- [The Influence Function of Semiparametric Estimators](https://mlsanity.com/paper/1508.01378/) (2015)
- [Kernel Methods for Causal Functions: Dose, Heterogeneous, and Incremental Response Curves](https://mlsanity.com/paper/2010.04855/) (2020)
- [Adversarial Estimation of Riesz Representers](https://mlsanity.com/paper/2101.00009/) (2020)
- [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)
- [Competitive Gradient Descent](https://mlsanity.com/paper/1905.12103/) (2019)
- [Debiased Machine Learning without Sample-Splitting for Stable Estimators](https://mlsanity.com/paper/2206.01825/) (2022)
- [Conservative Stochastic Optimization with Expectation Constraints](https://mlsanity.com/paper/2008.05758/) (2020)
- [Variable importance measures for heterogeneous treatment effects](https://mlsanity.com/paper/2204.06030/) (2022)
- [A Neural Mean Embedding Approach for Back-door and Front-door Adjustment](https://mlsanity.com/paper/2210.06610/) (2022)
- [Incremental causal effects](https://mlsanity.com/paper/1907.13258/) (2019)

## Built on by (most cited first, 2 of 2)

- [Learning density ratios in causal inference using Bregman-Riesz regression](https://mlsanity.com/paper/2510.16127/) (2025)
- [Outcome-adapted Automatic Debiased Machine Learning](https://mlsanity.com/paper/2607.03351/) (2026)

## Abstract (arXiv)

Causal and nonparametric estimands in economics and biostatistics can often be viewed as the mean of a linear functional applied to an unknown outcome regression function. Naively learning the regression function and taking a sample mean of the target functional results in biased estimators, and a rich debiasing literature has developed where one additionally learns the so-called Riesz representer (RR) of the target estimand (targeted learning, double ML, automatic debiasing etc.). Learning the RR via its derived functional form can be challenging, e.g. due to extreme inverse probability weights or the need to learn conditional density functions. Such challenges have motivated recent advances in automatic debiasing (AD), where the RR is learned directly via minimization of a bespoke loss. We propose moment-constrained learning as a new RR learning approach that addresses some shortcomings in AD, constraining the predicted moments and improving the robustness of RR estimates to optimization hyperparamters. Though our approach is not tied to a particular class of learner, we illustrate it using neural networks, and evaluate on the problems of average treatment/derivative effect estimation using semi-synthetic data. Our numerical experiments show improved performance versus state of the art benchmarks.