Riesz representers for the rest of us

2025/07/25 by Nicholas T. Williams, Williams, Nicholas T., Oliver J. Hines +3
#FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2507.19413

Abstract

The application of semiparametric efficient estimators, particularly those that leverage machine learning, is rapidly expanding within epidemiology and causal inference. This literature is increasingly invoking the Riesz representation theorem and Riesz regression. This paper aims to introduce the Riesz representation theorem to an epidemiologic audience, explaining what it is and why it's useful, using step-by-step worked examples.

Citations

• Learning density ratios in causal inference using Bregman-Riesz regression
• Pulling back the curtain: the road from statistical estimand to machine-learning based estimator for epidemiologists (no wizard required)
• RieszBoost: Gradient Boosting for Riesz Regression
• Automatic debiasing of neural networks via moment-constrained learning
• General targeted machine learning for modern causal mediation analysis
• Longitudinal Generalizations of the Average Treatment Effect on the Treated for Multi-valued and Continuous Treatments
• Application of targeted maximum likelihood estimation in public health and epidemiological studies: a systematic review
• Semiparametric doubly robust targeted double machine learning: a review
• The Balancing Act in Causal Inference
• RieszNet and ForestRiesz: Automatic Debiased Machine Learning with Neural Nets and Random Forests
• Automatic Debiased Machine Learning via Riesz Regression
• Non-parametric causal effects based on longitudinal modified treatment policies
• A Fundamental Measure of Treatment Effect Heterogeneity
• Visually Communicating and Teaching Intuition for Influence Functions
• Automatic Debiased Machine Learning of Causal and Structural Effects
• Automatic Debiased Machine Learning of Causal and Structural Effects
• Overlap in Observational Studies with High-Dimensional Covariates
• Adam: A Method for Stochastic Optimization
• Doubly Robust Estimation of Causal Effects
• Doubly Robust Estimation in Missing Data and Causal Inference Models
• Direct and Indirect Effects
• Direct and Indirect Effects
• Estimation of Regression Coefficients When Some Regressors are not Always Observed
• The central role of the propensity score in observational studies for causal effects
• Estimating causal effects of treatments in randomized and nonrandomized studies.
• A Generalization of Sampling Without Replacement from a Finite Universe

Related

• RieszBoost: Gradient Boosting for Riesz Regression
• Riesz Regression As Direct Density Ratio Estimation
• A Unified Theory for Causal Inference: Direct Debiased Machine Learning via Bregman-Riesz Regression
• Adversarial Estimation of Riesz Representers
• ScoreMatchingRiesz: Auto-DML with Infinitesimal Classification