arxiv_ml 80% Match Theoretical Note/Paper Researchers in causal inference,Statisticians,Econometricians 1 week ago

A Unified Theory for Causal Inference: Direct Debiased Machine Learning via Bregman-Riesz Regression

graph-neural-networks › graph-learning

📄 Abstract

Abstract: This note introduces a unified theory for causal inference that integrates Riesz regression, covariate balancing, density-ratio estimation (DRE), targeted maximum likelihood estimation (TMLE), and the matching estimator in average treatment effect (ATE) estimation. In ATE estimation, the balancing weights and the regression functions of the outcome play important roles, where the balancing weights are referred to as the Riesz representer, bias-correction term, and clever covariates, depending on the context. Riesz regression, covariate balancing, DRE, and the matching estimator are methods for estimating the balancing weights, where Riesz regression is essentially equivalent to DRE in the ATE context, the matching estimator is a special case of DRE, and DRE is in a dual relationship with covariate balancing. TMLE is a method for constructing regression function estimators such that the leading bias term becomes zero. Nearest Neighbor Matching is equivalent to Least Squares Density Ratio Estimation and Riesz Regression.

Authors (1)

Masahiro Kato

Submitted

October 30, 2025

arXiv Category

stat.ML

arXiv PDF

Key Contributions

This paper unifies several existing methods for causal inference, including Riesz regression, covariate balancing, density-ratio estimation, TMLE, and matching estimators, under a single theoretical framework. This unification simplifies understanding and potentially leads to more robust and efficient estimation of causal effects by highlighting dual relationships and special cases among these techniques.

Business Value

Provides a more robust theoretical foundation for understanding and estimating causal relationships in data, which is crucial for decision-making in fields like marketing, policy evaluation, and healthcare.

Paper Metadata

Innovation Type

Theoretical Unification

Deployment Feasibility

High, as it's a theoretical framework that can be implemented using existing statistical and machine learning tools.

Limitations Addressed

Addresses the fragmentation of methods for causal inference and provides a unified perspective that can lead to better understanding and application of these techniques.

Technical Tags

causal inferenceRiesz regressioncovariate balancingdensity-ratio estimationTMLEATE estimationbias correctionmachine learning

Research Topics

Causal InferenceStatistical LearningMachine Learning TheoryEconometrics

Methods & Architectures

Riesz regressioncovariate balancingdensity-ratio estimation (DRE)targeted maximum likelihood estimation (TMLE)matching estimatorBregman-Riesz Regression

Applications & Tasks

Statistics Econometrics Social Sciences Causal Effect EstimationBias Reduction Average Treatment Effect (ATE) estimation

Related Fields

StatisticsMachine LearningEconometricsEpidemiology

Keywords

causal inferenceRiesz regressioncovariate balancingdensity-ratio estimationTMLEATEbias correctionmachine learningstatistical learningeconometricsunified theory

Academic Context

#Causal Inference#Statistical Learning#Machine Learning Theory#Econometrics

Commercial Potential

Competitive Edge

Offers a unifying theoretical perspective over disparate methods in causal inference.

Resource Requirements

Compute Needs

Low

Data Requirements

Requires data suitable for causal inference tasks.

Scalability

The theoretical framework is general and can be applied to large datasets.

Production Readiness

Maturity Level

Theoretical

Patent Potential

Low

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