# Direct Debiased Machine Learning via Bregman Divergence Minimization

arXiv: https://arxiv.org/abs/2510.23534 · HTML: https://mlsanity.com/paper/2510.23534/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 50 references that are in the map.
- First posted on arXiv 27 Oct 2025.

## Builds on (most cited first, 13 of 13)

- [Positive-Unlabeled Learning with Non-Negative Risk Estimator](https://mlsanity.com/paper/1703.00593/) (2017)
- [Telescoping Density-Ratio Estimation](https://mlsanity.com/paper/2006.12204/) (2020)
- [Rethinking Importance Weighting for Deep Learning under Distribution Shift](https://mlsanity.com/paper/2006.04662/) (2020)
- [Non-Negative Bregman Divergence Minimization for Deep Direct Density Ratio Estimation](https://mlsanity.com/paper/2006.06979/) (2020)
- [Covariate Balancing Propensity Score by Tailored Loss Functions](https://mlsanity.com/paper/1601.05890/) (2016)
- [Off-Policy Evaluation and Learning for External Validity under a Covariate Shift](https://mlsanity.com/paper/2002.11642/) (2020)
- [Augmented balancing weights as linear regression](https://mlsanity.com/paper/2304.14545/) (2023)
- [Automatic Debiased Machine Learning for Covariate Shifts](https://mlsanity.com/paper/2307.04527/) (2023)
- [Kernel Balancing: A flexible non-parametric weighting procedure for estimating causal effects](https://mlsanity.com/paper/1605.00155/) (2016)
- [Direct Bias-Correction Term Estimation for Average Treatment Effect Estimation](https://mlsanity.com/paper/2509.22122/) (2025)
- [Learning Causal Models from Conditional Moment Restrictions by Importance Weighting](https://mlsanity.com/paper/2108.01312/) (2021)
- [Double Debiased Covariate Shift Adaptation Robust to Density-Ratio Estimation](https://mlsanity.com/paper/2310.16638/) (2023)
- [Density-Ratio Based Personalised Ranking from Implicit Feedback](https://mlsanity.com/paper/2101.07481/) (2021)

## Built on by (most cited first, 5 of 5)

- [Nearest Neighbor Matching as Least Squares Density Ratio Estimation and Riesz Regression](https://mlsanity.com/paper/2510.24433/) (2025)
- [Riesz Regression As Direct Density Ratio Estimation](https://mlsanity.com/paper/2511.04568/) (2025)
- [A Unified Theory for Causal Inference: Direct Debiased Machine Learning via Bregman-Riesz Regression](https://mlsanity.com/paper/2510.26783/) (2025)
- [Semi-Supervised Treatment Effect Estimation with Unlabeled Covariates for Prediction-Powered Causal Inference](https://mlsanity.com/paper/2511.08303/) (2025)
- [Bridging the Gap between Empirical Welfare Maximization and Conditional Average Treatment Effect Estimation in Policy Learning](https://mlsanity.com/paper/2510.26723/) (2025)

## Abstract (arXiv)

We develop a direct debiased machine learning framework comprising Neyman targeted estimation and generalized Riesz regression. Our framework unifies Riesz regression for automatic debiased machine learning, covariate balancing, targeted maximum likelihood estimation (TMLE), and density-ratio estimation. In many problems involving causal effects or structural models, the parameters of interest depend on regression functions. Plugging regression functions estimated by machine learning methods into the identifying equations can yield poor performance because of first-stage bias. To reduce such bias, debiased machine learning employs Neyman orthogonal estimating equations. Debiased machine learning typically requires estimation of the Riesz representer and the regression function. For this problem, we develop a direct debiased machine learning framework with an end-to-end algorithm. We formulate estimation of the nuisance parameters, the regression function and the Riesz representer, as minimizing the discrepancy between Neyman orthogonal scores computed with known and unknown nuisance parameters, which we refer to as Neyman targeted estimation. Neyman targeted estimation includes Riesz representer estimation, and we measure discrepancies using the Bregman divergence. The Bregman divergence encompasses various loss functions as special cases, where the squared loss yields Riesz regression and the Kullback-Leibler divergence yields entropy balancing. We refer to this Riesz representer estimation as generalized Riesz regression. Neyman targeted estimation also yields TMLE as a special case for regression function estimation. Furthermore, for specific pairs of models and Riesz representer estimation methods, we can automatically obtain the covariate balancing property without explicitly solving the covariate balancing objective.