Riesz Representer

TL;DR In the paper Automatic Debiased Machine Learning via Riesz Regression by Chernozhukov et al. (2024), the critical radius is a key concept for understanding how accurately machine learning (ML) can estimate the Riesz representer—a function used to debias ML estimates of economic parameters like treatment effects.

Introduction Here are my notes on propensity scores, mainly from Prof. Ding’s textbook (2024). The traditional propensity score analysis workflow is shown in the image below, which I will not cover in detail.

Introduction To estimate ATE, we can either use outcome regression or inverse propensity weighting (IPW). While each approach has merits, combining them offers significant advantage – double robustness. In this post, I summarize the intuition for doubly robust estimator from Professor Ding’s awesome textbook (Ding, 2024), and connects this framework to debiased machine learning (DML) through Riesz representation theory.

Debiased machine learning (DML) is a generic recipe. The idea behind it is adding a correction term to the plug-in estimator of the functional, which leads to properties such as semi-parametric efficiency, double robustness, and Neyman orthogonality.